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Household’s Budget Line

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1. What does a household’s budget line show? The budget line plots combinations of goods that require all a household’s income and describes the limits to its consumption choices. 2. How does the relative price and a household’s real income influence its budget line? The magnitude of the slope of the budget line equals the relative price of the good or service measured on the horizontal axis.

A fall in the price of the good measured on the horizontal (vertical) axis decreases that good’s relative price and decreases (increases) the slope of the budget line.

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A household’s real income is the household’s income expressed as a quantity of goods the household can afford to buy. An increase (decrease) in household income causes a parallel shift of the budget line rightward (leftward). The slope of the budget line does not change when income changes. 3. If a household has an income of $40 and buys only bus rides at $2 each and magazines at $4 each, what is the equation of the household’s budget line?

The budget equation states that a consumer’s spending must equal his or her income.

The budget equation is derived for two goods, bus rides and magazines. The amount spent on bus rides is (Pbus ride)(Qbus ride), the amount spent on magazines is (Pmagazine)(Qmagazine), and the consumer’s income is y. We know that (Pmagazine)(Qmagazine) + (Pbus ride)(Qbus ride) = y. Rearrange this equality by subtracting the amount spent on bus rides from both sides to give (Pmagazine)(Qmagazine) = y – (Pbus ride)(Qbus ride).

Finally, divide both sides by the price of magazine to give the budget equation Qmagazine = y/Pmagazine – (Pbus ride /Pmagazine)(Qbus ride). Substituting in our values, y = $40, P bus ride = $2 and P magazine = $4, gives Qmagazine = $40/$4 – ($2/$4)(Qbus ride) which is equal to Qmagazine = 10 – 0. 5 Qbus ride 4. If the price of one good changes, what happens to the relative price and the slope of the household’s budget line? A relative price is the price of one good divided by the price of another good. For example, the magnitude of the slope of the budget line (Pmovie/Psoda) is the relative price of a movie in terms of soda.

This relative price shows how many sodas must be forgone to see an additional movie. A fall in the price of the good on the horizontal (vertical) axis increases the total affordable quantity of that good, decreases its relative price, and decreases (increases) the magnitude of the slope of the budget line. 5. If a household’s money income changes and prices do not change, what happens to the household’s real income and budget line? A household’s real income is the household’s income expressed as a quantity of goods the household can afford to buy.

For example, the vertical intercept for a budget line measuring soda on the vertical axis is (y/Psoda), which is the consumer’s real income in terms of sodas. A change in a household’s money income changes the household’s real income in terms of both goods and causes a parallel shift of the budget line. If a household’s money income increases, its budget line shifts rightward and if a household’s money income decreases, it budget line shifts leftward. Page 210 1. What is an indifference curve and how does a preference map show preferences?

An indifference curve shows those combinations of goods for which a consumer is indifferent. The consumer has the same level of satisfaction for any combination on a given indifference curve. The family of indifference curves is the preference map. This map shows the person’s preferences because it shows how the person ranks each combination of goods. 2. Why does an indifference curve slope downward and why is it bowed toward the origin? The downward slope of an indifference curve illustrates the tradeoff between two goods while maintaining the same level of total satisfaction.

Since the consumer is indifferent among all points on an indifference curve, when moving along it any increase in satisfaction from gaining one good must be matched by an equal decrease in satisfaction from a loss in the other good. An indifference curve is bowed toward the origin because the more of good x that is consumed the less you are willing to give up of good y to get more of good x and remain indifferent. 3. What do we call the magnitude of the slope of an indifference curve? The magnitude of the slope of an indifference curve is called the marginal rate of substitution (MRS).

The MRS measures the rate at which the consumer gives up one good to get more of another good, while remaining on the same indifference curve (keeping the consumer indifferent about the changes). The ratio of the quantity of one good needed to replace the quantity of the other good and remain indifferent is the slope of the indifference curve. The bowed-in shape of the indifference curve is due to the assumption of diminishing MRS. 4. What is the key assumption about a consumer’s marginal rate of substitution?

The key assumption about the marginal rate of substitution is that it is diminishing as a consumer moves down an indifference curve, creating the bowed-in shape. Page 214 1. When a consumer chooses the combination of goods and services to buy, what is she or he trying to achieve? The consumer is trying to achieve the highest level of well being possible. 2. Explain the conditions that are met when a consumer has found the best affordable combination of goods to buy. (Use the terms budget line, marginal rate of substitution, and relative price in your explanation. At the optimal consumption choice, the consumer’s consumption bundle is 1)on the budget line, 2)on the highest attainable indifference curve, 3)such that the slope of the budget line, which is the relative price of the two goods, equals the slope of the indifference curve, which is the MRS. 3. If the price of a normal good falls, what happens to the quantity demanded of that good? If the price of a normal good falls, the quantity demanded of that good increases because the substitution effect and the income effect both bring an increase in the quantity demanded. 4.

Into what two effects can we divide the effect of a price change? A price change can be divided into a substitution effect and an income effect. The substitution effect is the effect of a change in price on the quantity bought when the consumer remains indifferent between the original situation and the new situation. The income effect is the effect of a change in income sufficient to get the consumer to the highest indifference curve that is affordable on the new budget line reflecting the price change. 5. For a normal good, does the income effect reinforce the substitution effect or does it partly offset the substitution effect?

For a normal good the substitution effect and the income effect reinforce each other, and a decrease (increase) in the price of a good will always result in an increase (decrease) in the quantity of the good demanded. Page 215 1. What is the opportunity cost of leisure? The opportunity cost of leisure is the income forgone when not working. 2. Why might a rise in the wage rate lead to an increase in leisure and a decrease in work hours? An increase in the wage rate increases the opportunity cost of leisure (not working).

The substitution effect means that a higher price for leisure motivates the person to substitute away from leisure and into labor (income). However, the income effect means that the higher level of income for the same amount of work allows the person to afford more leisure. If the income effect is stronger than the substitution effect, then the quantity of labor supplied decreases with the wage rate (negative sloped labor supply curve). Answers to the Problems and Applications 1. Sara’s income is $12 a week. The price of popcorn is $3 a bag, and the price of a smoothie is $3. a.

What is Sara’s real income in terms of smoothies? Sara’s real income is 4 smoothies. Sara’s real income in terms of smoothies is equal to her money income divided by the price of a smoothie. Sara’s money income is $12, and the price of a smoothie is $3. Sara’s real income is $12 divided by $3 a smoothie, which is 4 smoothies. b. What is her real income in terms of popcorn? Sara’s real income is 4 bags of popcorn. Sara’s real income in terms of popcorn is equal to her money income divided by the price of a bag of popcorn, which is $12 divided by $3 a bag or 4 bags of popcorn. c.

What is the relative price of smoothies in terms of popcorn? The relative price of a smoothie is 1 bag of popcorn per smoothie. The relative price of a smoothie is the price of a smoothie divided by the price of a bag of popcorn. The price of a smoothie is $3 and the price of popcorn is $3 a bag, so the relative price of a smoothie is $3 divided by $3 a bag, which equals 1 bag of popcorn per smoothie. d. What is the opportunity cost of a smoothie? The opportunity cost of a smoothie is 1 bag of popcorn. The opportunity cost of a smoothie is the quantity of popcorn that must be forgone to get a smoothie.

The price of a smoothie is $3 and the price of popcorn is $3 a bag, so to buy one smoothie Sara must forgo 1 bag of popcorn. e. Calculate the equation for Sara’s budget line (with bags of popcorn on the left side). The equation that describes Sara’s budget line is QP = 4 – QS. Call the price of popcorn PP and the quantity of popcorn QP, the price of a smoothie PS and the quantity of smoothies QS, and income y. Sara’s budget equation is PPQP + PSQS = y. If we substitute $3 for the price of popcorn, $3 for the price of a smoothie, and $12 for the income, the budget equation becomes $3QP + $3QS = $12.

Dividing both sides by $3 and subtracting QS from both sides gives QP = 4 – QS. f. Draw a graph of Sara’s budget line with quantity of smoothies on the x-axis. To draw a graph of the budget line, plot the quantity of smoothies on the x-axis and the quantity of popcorn on the y-axis. The budget line is a straight line from 4 bags of popcorn on the y-axis to 4 smoothies on the x-axis. g. In part f, what is the slope of Sara’s budget line? What determines its value? The slope of the budget line, when smoothies are plotted on the x-axis, is minus 1.

The magnitude of the slope is equal to the relative price of a smoothie. The slope of the budget line is “rise over run. ” If the quantity of smoothies decreases from 4 to 0, the quantity of popcorn increases from 0 to 4. The rise is 4 and the run is ? 4. Therefore the slope equals 4/? 4, which is ? 1. 2. Sara’s income falls from $12 a week to $9 a week, while the price of popcorn remains at $3 a bag and the price of a smoothie remains at $3. a. What is the effect of the fall in Sara’s income on her real income in terms of smoothies?

Sara’s real income falls from 4 smoothies to 3 smoothies. Sara’s real income in terms of smoothies is equal to her money income divided by the price of a smoothie. Sara’s money income is now $9 and the price of smoothie is $3. Sara’s real income is now $9 divided by $3 a smoothie, which is 3 smoothies. b. What is the effect of the fall in Sara’s income on her real income in terms of popcorn? Sara’s real income falls from 4 bags of popcorn to 3 bags of popcorn. Sara’s real income in terms of popcorn is equal to her money income divided by the price of a bag of popcorn.

Sara’s money income is now $9 and the price of bag of popcorn is $3. Sara’s real income is now $9 divided by $3 a bag, which is 3 bags of popcorn. c. What is the effect of the fall in Sara’s income on the relative price of a smoothie in terms of popcorn? The relative price of a smoothie is 1 bag of popcorn per smoothie, the same relative price as before her income fell. The relative price does not depend on Sara’s income. Instead the relative price of a smoothie is the price of a smoothie divided by the price of a bag of popcorn.

The price of a smoothie is $3 and the price of popcorn is $3 a bag, so the relative price of a smoothie is $3 divided by $3 a bag. The relative price equals 1 bag per smoothie. d. What is the slope of Sara’s new budget line if it is drawn with smoothies on the x-axis? The slope of the budget line, when smoothies are plotted on the x-axis is minus 1, the same slope as before her fall in income. The magnitude of the slope of the budget line is equal to the relative price of a smoothie. The relative price does not change when Sara’s income decreases so the slope of the budget line does not change. . Sara’s income is $12 a week. The price of popcorn rises from $3 to $6 a bag, and the price of smoothie remains at $3. a. What is the effect of the rise in the price of popcorn on Sara’s real income in terms of smoothies? The rise in the price of a bag of popcorn has no effect on Sara’s real income in terms of smoothies. Sara’s real income in terms of smoothies remains 4 smoothies. b. What is the effect of the rise in the price of popcorn on Sara’s real income in terms of popcorn? Sara’s real income in terms of popcorn falls to 2 bags of popcorn.

Sara’s real income in terms of popcorn is equal to her money income divided by the price of a bag of popcorn. Sara’s money income is $12 and the price of a bag of popcorn is now $6. Sara’s real income is now $12 divided by $6 a bag, which is 2 bags of popcorn. c. What is the effect of the rise in the price of popcorn on the relative price of a smoothie in terms of popcorn? The relative price of a smoothie falls to 1/2 bag of popcorn per smoothie. The relative price of a smoothie is the price of a smoothie divided by the price of a bag of popcorn.

The price of a smoothie is $3 and the price of popcorn is $6 a bag, so the relative price of a smoothie is $3 divided by $6 a bag, which equals 1/2 bag of popcorn per smoothie. The rise in the price of a bag of popcorn lowers the relative price of a smoothie in terms of popcorn. d. What is the slope of Sara’s new budget line if it is drawn with smoothies on the x-axis? The slope of the budget line, when smoothies are plotted on the x-axis is minus 1/2. The magnitude of the slope is equal to the relative price of a smoothie. The relative price has fallen so the magnitude of the slope of the budget line has fallen. . The Year in Medicine Sudafed, used to clear up those autumn sniffles, … contains as one of its active ingredients pseudoephedrine, widely used in backyard labs to make methamphetamine. … Now, allergy sufferers looking for relief have to ask a pharmacist or salesclerk for their Sudafed, show photo ID, and sign a logbook. Unfortunately, the most common alternative, phenylephrine, isn’t as effective. Time, December 4, 2006 a. Draw an indifference curve for Sudafed and phenylephrine that is consistent with this news clip. Figure 9. 2 has an indifference curve, I. b.

On your graph in part a, identify combinations that allergy sufferers prefer, do not prefer, and are indifferent among. Figure 9. 2 shows the preferred, not preferred, and indifferent points. The preferred points are all points to the right of the indifference curve; the not preferred points are all points to the left of the indifference curve; and, the indifferent points are all points on the indifference curve. c. Explain how the marginal rate of substitution changes along this indifference curve. The marginal rate of substitution falls moving downward along the indifference curve. . Draw figures that show your indifference curves for the following pairs of goods: • Right gloves and left gloves • Coca-Cola and Pepsi • Baseballs and baseball bats • Tylenol and acetaminophen (the generic form of Tylenol) • Eye glasses and contact lenses • Desktop computers and laptop computers • Skis and ski poles a. For each pair, state whether the goods are perfect substitutes, perfect complements, or neither. Right gloves/left gloves and skis/ski poles are perfect complements. The other pairs are neither perfect substitutes nor perfect complements. . Discuss the shape of the indifference curve you have drawn and explain the relationship between its shape and the marginal rate of substitution as the quantities of the two goods change. Right and left gloves: These are perfect complements, so the indifference curves are right angles, such as those in Figure 9. 3A. The marginal rate of substitution does not change moving down along the indifference curve except when moving around the 90 degree point where it goes from infinity to zero. Coca-Cola and Pepsi: These are, for most students, almost perfect substitutes.

The indifference curves should either be linear (for perfect substitutes, as shown in Figure 9. 3B) or nearly linear. If the indifference curves are linear, then the marginal rate of substitution does not change moving down along the indifference curve; if the indifference curves are nearly linear, then the marginal rate of substitution falls slightly moving down along an indifference curve. Baseball balls and bats: These are complements but probably not perfect complements. The indifference curves should be significantly bowed inward as in Figure 9. 3C. If a student says these goods are perfect complements, the indifference curves should be right angles, such as those in Figure 9. 3A. ) If the indifference curves are not right angles, then the marginal rate of substitution falls rapidly moving down along an indifference curve. (If the goods are perfect complements, the marginal rate of substitution does not change moving down along the indifference curve except when moving around the 90 degree point where it goes from infinity to zero. ) Tylenol and acetaminophen: These are, for most people, very close substitutes.

For some consumers, they might be perfect substitutes. The indifference curves should either be linear (for perfect substitutes, as shown in Figure 9. 3B) or nearly linear as in Figure 9. 3D. If the indifference curves are linear, then the marginal rate of substitution does not change moving down along the indifference curve; if the indifference curves are nearly linear, then the marginal rate of substitution falls slightly moving down along an indifference curve. Eye glasses and contact lenses: These are substitutes, though probably not perfect substitutes.

The indifference curve are slightly bowed inward toward the origin as in Figure 9. 3E. The marginal rate of substitution falls slightly moving down along an indifference curve. Desktop computers and laptop computers; These are substitutes, though not perfect substitutes. The indifference curve are bowed inward toward the origin as in Figure 9. 3F. The marginal rate of substitution falls moving down along an indifference curve. Skis and ski poles: These are perfect complements. The indifference curves are right angles, such as those in Figure 9. 3G.

The marginal rate of substitution does not change moving down along the indifference curve except when moving around the 90 degree point where it goes from infinity to zero. 6. Pam has chosen her best affordable combination of cookies and comic books. She has spent all of her income on 30 cookies at $1 each and 5 comic books at $2 each. Next month, the price of a cookie falls to 50? and the price of a comic book rises to $5. a. Will Pam be able to buy and want to buy 30 cookies and 5 comic books next month? Pam can still buy 30 cookies and 5 comic books. When Pam buys 30 cookies at $1 each and 5 comic books at $2 each, she spends $40 a month.

Now that the price of a cookie is 50 cents and the price of a comic book is $5, 30 cookies and 5 comic books will cost $40. So Pam can still buy 30 cookies and 5 comic books. But Pam will not want to buy 30 cookies and 5 comic books because the marginal rate of substitution does not equal the relative price of the goods. Pam will move to a point on the highest indifference curve possible where the marginal rate of substitution equals the relative price. b. Which situation does Pam prefer: cookies at $1 and comic books at $2 or cookies at 50? and comic books at $5?

Pam prefers cookies at 50 cents each and comic books at $5 each because she can get onto a higher indifference curve than when cookies are $1 each and comic books are $2 each. To see why Pam can move to a higher indifference curve, note that the new budget line and the old budget line both pass through the point 30 cookies and 5 comic books. If comic books are plotted on the x-axis, the marginal rate of substitution at this point on Pam’s indifference curve is equal to the relative price of a comic book at the original prices, which is 2. The new relative price of a comic book is $5/50 cents, which is 10.

That is, the budget line is steeper than the indifference curve at 30 cookies and 5 comic books. So Pam’s new equilibrium combination of cookies and comic books must be on an indifference curve at a point steeper than the initial indifference curve. Because the new budget line is steeper and passes through the initial equilibrium combination, the new equilibrium must lie above the initial equilibrium point so it must be on a higher indifference curve. c. If Pam changes the quantities that she buys, will she buy more or fewer cookies and more or fewer comic books.

Pam will buy more cookies and fewer comic books. The new budget line and the old budget line pass through the point at 30 cookies and 5 comic books. If comic books are plotted on the x-axis, the marginal rate of substitution at this point on Pam’s indifference curve is equal to the relative price of a comic book at the original prices, which is 2. The new relative price of a comic book is $5/50 cents, which is 10. That is, the budget line is steeper than the indifference curve at 30 cookies and 5 comic books. Pam will buy more cookies and fewer comic books. . When the prices change next month, will there be an income effect and a substitution effect at work or just one of them? There will be a substitution effect and an income effect. A substitution effect arises when the relative price changes and the consumer moves along the same indifference curve to a new point where the marginal rate of substitution equals the new relative price. An income effect arises when the consumer moves from one indifference curve to another, keeping the relative price constant. 7. Boom Time For ‘Gently Used’ Clothes

Unlike most retailers who are blaming the economy for their poor sales, one store chain is boldly declaring that an economic downturn can actually be a boon for its business. … [It] sells used name-brand children’s clothes, toys, and furniture. … Last year, the company took in $20 million in sales, up 5% from the previous year. “Our sales are already up 5% so far this year. ” CNN, April 17, 2008 a. According to this article, is used clothing a normal good or inferior good? According to the article, the demand for used clothing increases when the economy is in a downturn and incomes are falling.

Because the demand increases when income decreases, used clothing is an inferior good. b. If the price of used clothing falls and income remains the same, explain how the quantity of used clothing bought changes If the price of used clothing falls and income remains the same, the quantity of used clothing purchased increases. c. If the price of used clothing falls and income remains the same, describe the substitution effect and the income effect that occur. The price fall creates both a substitution effect and an income effect. The substitution effect leads to an increase in the quantity of used clothing demanded.

The price decrease increases consumers’ real incomes. Because used clothing is an inferior good, the income effect leads to a decrease in the quantity of used clothing purchased. The substitution effect is larger so that the quantity of used clothing purchased increases. d. Draw a graph to illustrate a family’s indifference curves for used clothing and other goods and services. Figure 9. 4 shows a family’s indifference curves for used clothing and other goods and services. e. In your graph in d, draw two budget lines to show the effect of a fall in income on the quantity of used clothing purchased.

In Figure 9. 3, the fall in income shifts the budget line from BL1 to BL2. The quantity of used clothing purchased increases, in the figure from 4 items per month to 5 items per month. 8. Gas Prices to Stunt Memorial Day Travel 12% have cancelled road trips altogether. … 11% of respondents will be vacationing closer to home this weekend. … That may save consumers some money, but it will also likely … hurt on a variety of businesses that serve the traveler. Service stations will suffer as they not only presumably sell less gas, but also fewer snacks, drinks and sundry items. .. Hotel chains, especially those with a heavy roadside presence [suffer]. … Also under pressure are casual-dining chains that rely heavily on highway traffic. … MarketWatch, May 22, 2008 a. Describe the degree of substitutability between gasoline and roadside hotels and draw a preference map to illustrate your description. Gasoline and roadside hotels are complements. Figure 9. 6 (on the next page) shows the indifference curves. Because gasoline and roadside motels are complements, so the indifference curves are right angles. b.

Draw a budget line for gasoline and roadside hotels and identify the best affordable point. Figure 9. 7 shows the budget line, BL0. The best affordable point is 75 gallons of gasoline and 3 stays at roadside hotels. c. Show on your graph how the best affordable point changes when the price of gasoline rises. When the price of gasoline rises, Figure 9. 7 shows that the budget line rotates from BL0 to BL1. The best affordable point changes from 75 gallons of gasoline and 3 stays at roadside hotels to 50 gallons of gasoline and 2 stays at roadside hotels. 9. Does a Second Income Pay?

When considering whether two paychecks are worth it, figure out how much of the lower earner’s salary will be eaten by expenses incurred if both parents work. Childcare is likely to be the biggest cost. … Also, take into account the costs of going to work. The commute, the clothes, the dry cleaning, the lunches. … And you may not have as much time or energy to do the housework or make dinner. So you may end up hiring a housekeeper or doing take-out more often. … CNN, March 15, 2006 a. What is the opportunity cost of a parent staying home with her or his children?

The opportunity cost of staying home with the children is the earned income forgone. b. What is the opportunity cost of a parent working instead of staying home? The monetary opportunity cost of a parent working include the childcare cost, the cost of the commute, the cost of a housekeeper, the clothes, the dry cleaning, the lunches, and the dinners out. Of course, the opportunity cost includes only the part of the cost of the clothes, the dry cleaning, the lunches, and the dinners out that was incurred because the person was working.

An additional opportunity cost for a family with offspring is the time that is no longer spent with the child or children. c. Why does the opportunity cost of working increase as the number of children in a family increases? The cost of childcare, an opportunity cost of working increases as the number of children increases. d. How does the number of children in a family influence the marginal rate of substitution between leisure and goods and services? The greater the number of children in a family, the higher the opportunity cost of working.

Equivalently, the greater the number of children in a family, the lower the family’s income net of opportunity cost and hence the lower the net wage rate. The lower the wage rate, the smaller is the magnitude of the slope of the budget line. At the equilibrium point of time allocation, the slope of the indifference curve is equal to the slope of the budget line. Hence the smaller the magnitude of the slope of the budget line, the smaller the slope of the indifference curve and so the smaller the marginal rate of substitution between leisure and goods and services at the equilibrium point of time allocation. 10. Floyd Mayweather Jr.

Announces Retirement Unbeaten world champion boxer Floyd Mayweather Jr. backed out of negotiations for a September rematch against Oscar De La Hoya … announcing his retirement. … In May 2007, Mayweather Jr. won a split-decision over De La Hoya in a bout that established new records for pay-per-view and total revenue. … [De La Hoya’s business partner] didn’t believe Mayweather is employing a tactic to earn more money in a De La Hoya fight. … “He has made enough money to live comfortably for the rest of his life, and if he wants to spend time with his babies, that’s a good thing …” Los Angeles Times, June 6, 2008 . Use the concepts of the substitution effect and the income effect to explain Mayweather’s decision. Mayweather’s decision to not supply his labor (in the fight) reflects the income effect from his bouts. The income effect—the fact that Mayweather made a huge amount of income in his previous bouts—influences him to decrease the quantity of labor he supplies. The substitution effect—the fact that Mayweather loses a huge amount of income if he opts for leisure rather than labor—influences him to increase the quantity of labor he supplies. Mayweather’s income effect is larger than his substitution effect. . At the income he earns per fight, is Mayweather’s labor supply curve upward-sloping or backward-bending? Mayweather’s labor supply curve is backward bending. c. Draw a graph of Mayweather’s indifference curves and budget line between leisure time and income and illustrate his decision to fight or not to fight. Show how an increase in the income per fight changes his decision. Figure 9. 8 shows Mayweather’s indifference curves and budget line. At a lower weekly wage rate for fighting, Mayweather’s budget line is BL0 and with indifference curve I0 he spends 40 hours per week preparing for the fight.

At the extraordinarily high wage Mayweather would receive for fighting again, his budget line becomes BL1, and Mayweather’s best time allocation point with indifference curve I1 has him using virtually his entire time taking leisure rather than fighting. 11. Gas Prices Straining Budgets …many say they are staying in and scaling back spending to try to keep up, … driving as little as possible, cutting back on shopping and eating out, and other discretionary spending. CNN, February 29, 2008 a. Draw a budget line for a household that consumes only two goods: gasoline and eating out.

Identify the combinations of gasoline and eating out that are affordable and those that are unaffordable. Figure 9. 9 shows a budget line. The combinations of gasoline and eating out that lie on and inside the budget line are affordable. The combinations of gasoline and eating out that lie beyond the budget line are unaffordable. b. Draw a second budget line to show how a rise in the price of gasoline changes the affordable and unaffordable combinations of gasoline and eating out. Describe how the household’s consumption possibilities change. The rise in the price of gasoline rotates the budget inward, as illustrated in Figure 9. 0. The combinations of gasoline and eating that were previously affordable that have now become unaffordable are shown by the grey triangle. The household’s consumption possibilities have been reduced. c. How does a rise in the price of gasoline change the relative price of eating out? The relative price of eating out equals the price of eating out divided by the price of gasoline. The rise in the price of gasoline reduces the relative price of eating out. d. How does a rise in the price of gasoline change real income in terms of eating out? The rise in the price of gasoline does not change real income in terms of eating out. 2. Rashid buys only books and albums and the figure shows his preferences. a. If Rashid chooses 3 books and 2 albums, what is his marginal rate of substitution? Rashid’s marginal rate of substitution is 1 book per album. Rashid’s marginal rate of substitution equals the magnitude of the slope of his indifference curve at his best affordable point. If Rashid buys 3 books and 2 albums, the slope of his indifference curve at this point is minus 1 book per album. b. If Rashid chooses 2 books and 6 albums, what is his marginal rate of substitution? Rashid’s marginal rate of substitution is 1/2.

Rashid’s marginal rate of substitution equals the magnitude of the slope of his indifference curve at his best affordable point. If Rashid buys 2 books and 6 albums, the slope of his indifference curve at this point is minus 1/2 book per album. c. Do Rashid’s indifference curves display a diminishing marginal rate of substitution? Explain why or why not. Rashid’s indifference curves display diminishing marginal rate of substitution because when moving along either indifference curve the slope becomes smaller as the consumption of albums increases. 13.

Sara’s income is $12 a week. The price of popcorn is $3 a bag, and the price of cola is $1. 50 a can. The figure shows Sara’s preference map for popcorn and cola. a. What quantities of popcorn and cola does Sara buy? Sara buys 6 cans of cola and 1 bag of popcorn. Sara’s budget line runs from 8 cans of cola on the x-axis to 4 bags of popcorn on the y-axis and is tangent to indifference curve I1 at 6 cans of cola and 1 bag of popcorn. b. What is Sara’s marginal rate of substitution at the point at which she consumes? Sara’s marginal rate of substitution is ?.

The marginal rate of substitution is the magnitude of the slope of the indifference curve at Sara’s consumption point, which equals the magnitude of the slope of the budget line. The slope of Sara’s budget line is ?? bag of popcorn per can of cola so the marginal rate of substitution is ? bag of popcorn per can of cola. 14. Now suppose that in problem 13, the price of cola rises to $3. 00 a can and the price of popcorn and Sara’s income remain the same. a. What quantities of cola and popcorn does Sara now buy? Sara buys 2 cans of cola and 2 bags of popcorn.

Sara buys the quantities of cola and popcorn that moves her onto the highest indifference curve, given her income and the (new) price of cola and price of popcorn. The budget line is tangent to indifference curve I0 at 2 cans of cola and 2 bags of popcorn. b. What are two points on Sara’s demand curve for cola? Draw Sara’s demand curve. Two points on Sara’s demand for cola are the following: At $3 a can of cola, Sara buys 2 cans of cola. At $1. 50 a can of cola, Sara buys 6 cans. Her demand curve is downward sloping and, as Figure 9. 13 shows, goes through these two points. c.

What is the substitution effect of this price change? The substitution effect is 1 can of cola. To divide the price effect into a substitution effect and an income effect, take enough income away from Sara and gradually move her new budget line back toward the original indifference curve until it just touches Sara’s first indifference curve I1. The point at which this budget line just touches indifference curve I1 is 5 cans of cola. The substitution effect is the decrease in the quantity of cola from 6 cans to 5 cans along the indifference curve I1. The substitution effect is 1 can of cola. . What is the income effect of this price change? The income effect is 3 cans of cola. The income effect is the change in the quantity of cola from the price effect minus the change from the substitution effect. The price effect is 4 cans of cola (2 cans minus the initial 6 cans). The substitution effect is a decrease in the quantity of cola from 6 cans to 5 cans. So the income effect is 3 cans of cola. e. Is cola a normal good or an inferior good? Cola is a normal good for Sara because the income effect is positive. 15. Jim has made his best affordable choice of muffins and coffee.

He spends all of his income on 10 muffins at $1 each and 20 coffees at $2 each. Now the price of a muffin rises to $1. 50 and the price of a coffee falls to $1. 75 a cup. a. Will Jim now be able and want to buy 10 muffins and 20 coffees? Jim is able to buy 10 muffins and 20 coffees because this combination remains affordable. Jim will not want to buy this combination, however, because the relative price of muffins and coffee has changed. At his consumer equilibrium, Jim’s MRS equals the relative price of muffins and coffee and because the relative price has changed, Jim’s MRS has changed so Jim will change his consumption point. . Which situation does Jim prefer: muffins at $1 and coffee at $2 a cup or muffins at $1. 50 and coffee at $1. 75 a cup? Jim prefers the $1. 50 per muffin/$1. 75 per coffee prices because he can attain a higher indifference curve. The new budget line goes through the old budget line at the initial consumption point. But, with coffee measured along the horizontal axis, the new budget line is flatter than the old budget line and lies beyond the initial budget line at all points below the initial consumption point. c.

If Jim changes the quantities that he buys, will he buy more or fewer muffins and more or less coffee? Jim will buy more coffee and fewer muffins. d. When the prices change, is there an income effect and a substitution effect at work or just one of them? Price changes can always be divided into an income effect and a substitution effect. 16. Rising Gas Costs Crimping Budgets More Americans are substituting higher-priced goods with cheaper ones—choosing McDonald’s coffee over Starbucks, for example, or hitting a bulk warehouse chain such as Costco or Sam’s Club instead of a pricier grocery store.

MSNBC, March 20, 2008 a. If an increase in the price of gasoline results in consumers substituting McDonald’s coffee for Starbucks coffee, what type of good is a McDonald’s coffee—normal or inferior? Explain. McDonald’s coffee is an inferior good. The rise in the price of gasoline decreases consumers’ real incomes and they respond to the decrease in income by increasing their demand for McDonald’s coffee. b. Draw a graph of an indifference curve and two budget lines to illustrate the effect of a rise in the price of gasoline on the quantity of coffee purchased from McDonald’s and from Starbucks. Figure 9. 4 shows the indifference curves and budget lines. With the inward shift of the budget line from BL0 to BL1 the consumer responds by decreasing purchases of Starbucks coffee from 3 cups per week to 1? cups per week and increasing purchases of McDonald’s coffee from 2 cups per week to 3 cups per week. 17. Gas Prices Send Surge of Travelers to Mass Transit With the price of gas approaching $4 a gallon, more commuters are abandoning their cars and taking the train or bus instead. … “It’s very clear that a significant portion of the increase in transit use is directly caused by people who are looking for alternatives to paying $3. 0 a gallon for gas. ” Some cities with long-established public transit systems, like New York and Boston, have seen increases in ridership of 5 percent or more so far this year. But the biggest surges — of 10 to 15 percent or more over last year — are occurring in many metropolitan areas in the South and West where the driving culture is strongest and bus and rail lines are more limited. The New York Times, May 10, 2008 a. Draw a graph of a preference map and a budget line to illustrate the best affordable combination of gasoline and public transit. Figure 9. 5 shows the initial indifference curve (I0) and initial budget line (BL0). The best affordable point is at point A with 100 gallons of gasoline and 15 rides on public transportation. b. On your graph in a, show the effect of a rise in the price of gasoline on the quantities of gasoline and public transit services purchased. In Figure 9. 15 the rise in the price of gasoline rotates the budget line from BL0 to BL1. The best affordable point moves to point B at which the quantity of gasoline purchased falls to 50 gallons per month and the quantity of rides on public transportation increases to 20 rides per month. . Assuming that the increase in the price of gasoline has been similar in all regions, compare the marginal rate of substitution in the Northeast to that in the South and West. Explain how you have inferred the different marginal rates of substitution from the information provided in the news clip. The story says the driving culture is strongest in the South and West and that bus and rail lines there are more limited. Presuming that the price of gasoline is the same nationwide, these statements mean that a budget line drawn for the South and West in Figure 9. 5 has the same vertical intercept but is steeper than a budget line drawn for the Northeast. At the consumer equilibrium the slope of the indifference curve equals the slope of the budget line, so the initial MRS in the South and West was higher than in the Northeast and residents in the South and West used more gasoline and less public transportation than in the Northeast. When the price of gasoline rises, the vertical intercept of both budget lines decreases by the same amount so the budget line in the South and West remains steeper than the budget line in the Northeast.

As a result the MRS in the South and West remains higher than the MRS in the Northeast. 18. You May Be Paid More (or Less) Than You Think It’s so hard to put a price on happiness, isn’t it? But if you’ve ever had to choose between a job you like and a better-paying one that you like less, you probably wished some economist would … tell you how much job satisfaction is worth. … Trust in management is by far the biggest component to consider. Say you get a new boss and your trust in management goes up a bit … (say, up one point on a 10-point scale). That’s like getting a 36 percent pay raise.

In other words, that increased level of trust will boost your level of overall satisfaction in life by about the same amount as a 36 percent raise would. CNN, March 29, 2006 a. Measure trust in management on a 10-point scale, measure pay on the same 10-point scale, and think of them as two goods. Draw an indifference curve (with trust on the x-axis) that is consistent with the information in the news clip. The clip implies that a 1 point increase in trust combined with a 3. 6 point (which is 36 percent on a 10 point scale) decrease in income leaves the person indifferent. So, as illustrated in Figure 9. 6 (on the next page) the indifference curve is linear showing the tradeoff between trust and income. b. What is the marginal rate of substitution between trust in management and pay according to this news clip? The news clip implies that the indifference curves are linear (as illustrated in Figure 9. 16) which means that the marginal rate of substitution is constant and equal to 3. 6 in the figure. c. What does the news clip imply about the principle of diminishing marginal rate of substitution? Is that implication likely to be correct? The news clip implies that the indifference curves are linear, as illustrated in Figure 9. 6. Linear in difference curves mean that the marginal rate of substitution is constant, that is, the principle of diminishing marginal rate of substitution does not hold. His assumption is likely to be incorrect. Increasing trust in management from 0 to 1 is likely to be very worthwhile and the person will give up a large amount of income to gain this unit increase. But increasing trust in management from, say, 8 to 9 is probably not nearly so worthwhile because at 8 management is already highly trusted. So to gain this unit increase in trust, the person is likely willing to give up only a small amount of income.

Hence, contrary to the article, increasing trust in management is subject to a diminishing rate of substitution. 19. Study Reading Between the Lines about music and e-book downloads on pp. 216–217, and then answer the following questions. a. How do you buy books? The answers will depend on how they buy books. b. Sketch your budget line for books and other goods. The budget line between paper books and other goods is a conventional downward sloping budget line and a sample is illustrated in Figure 9. 17. This budget line assumes the student has $800 to spend, the price of a print book is $20 and the price of each “other good” is $1.

If the student buys Amazon’s e-books, the student needs to buy a $360 Kindle with the first e-book. So the first e-book has a price of $370 and the rest of the e-books have a price of $10. The Kindle is non-divisible; that is, it is not possible to buy ? of a Kindle. As a result, with other goods on the vertical axis and e-books on the horizontal axis, the budget line shown in Figure 9. 18 starts at 800 “other goods” and 0 e-books and then jumps to 430 “other goods” and 1 e-book. The budget line is then more shallow to the maximum number of e-books, 44, to reflect the price of $10 per e-book for all the other e-books. . Sketch your indifference curves for books and other goods. The indifference curves will be conventional showing some substitutability between books and other goods. This is the situation illustrated in Figure 19. 19. d. What would happen to the way that you buy books if Amazon gave you its Kindle reader at a zero price if you buy just one e-book? If the student already purchases e-books and already has a Kindle, Amazon’s change in policy has no effect on the student’s budget line and hence does not change the student’s purchases.

If the student is a “committed print book lover” (as the first student analyzed on page 217) Amazon’s new policy changes the student’s budget line between print books and e-books (the budget line moves outward) but the policy change does not change the student’s purchases. For other students—those who have not yet purchased a Kindle and are not committed print book lovers—Amazon’s new policy changes the budget line (based on the budget line described in part b, the new budget line will be shallow everywhere reflecting the price of $10 per e-book for all e-books) and increases the number of e-books purchased. 0. The sales tax is a tax on goods. Some people say that a consumption tax, a tax on both goods and services, would be better. Explain and illustrate with a graph what would happen if we replaced the sales tax with a consumption tax to a. The relative price of books and haircuts. Books are goods and so are taxed under both a sales tax and a consumption tax. Haircuts are services and so are taxed only under a consumption tax. If the sales tax is replaced with a consumption tax, the relative price of a haircut rises and the relative price of a book falls. b.

The budget line showing the quantities of books and haircuts you can afford to buy. Assuming the sales tax and consumption tax are the same rate, in the figure the budget line rotates inward around a fixed book intercept. In Figure 9. 20 the new budget line is BL1. The price of a book does not change but the price of a haircut rises. c. Your purchases of books and haircuts. In general, if the relative price of a haircut rises and the relative price of a book falls, the substitution effect leads consumers to buy more books and fewer haircuts. There is, however, also an income effect.

The consumer’s real income falls, which decreases the demand for normal goods. Assuming that both books and haircuts are normal goods, then the income effect offsets the substitution effect of buying more books but reinforces the substitution effect of buying fewer haircuts. In Figure 9. 20, with the sales tax and budget line BL0 the consumer is initially at point A and buys 20 books per year and 4 haircuts per year. With the consumption tax and budget line BL1 the consumer moves to point B and buys 15 books per year and 3 haircuts per year. Additional Problems 1. Marc has an income of $20 per week.

Root beer costs $5 a can and CDs cost $10 each. a. What is Marc’s real income in terms of root beer? b. What is his real income in terms of CDs? c. What is the relative price of root beer in terms of CDs? d. What is the opportunity cost of a can of root beer? e. Calculate the equation for Marc’s budget line (placing cans of root beer on the left side). f. Draw a graph of Marc’s budget line with CDs on the x-axis. g. In part (f), what is the slope of Marc’s budget line? What does it equal? 2. Marc’s income and the prices he faces are the same as in problem 1. The figure illustrates his preferences. a.

What are the quantities of root beer and CDs that Marc buys? b. What is Marc’s marginal rate of substitution of CDs for root beer at the point at which he consumes? 3. Now suppose that in the situation described in problem 2, the price of a CD falls to $5 and the price of root beer and Marc’s income remain constant. a. Find the new quantities of root beer and CDs that Marc buys. b. Find two points on Marc’s demand curve for CDs. c. Find the substitution effect of the price change. d. Find the income effect of the price change. e. Are CDs a normal good or an inferior good for Marc? 4. Pete buys tuna and golf balls.

The price of tuna is $2 a can, and the price of a golf ball is $1. Each month, Pete spends all of his income and buys 20 cans of tuna and 40 golf balls. Next month, the price of tuna will rise to $3 a can and the price of a golf ball will fall to 50?. Assume that Pete’s preference map shows indifference curves that have a similar shape to that in Fig. 9. 3(b). a. Will Pete be able to buy 20 cans of tuna and 40 golf balls next month? b. Will Pete want to buy 20 cans of tuna and 40 golf balls? c. Which situation does Pete prefer: tuna at $2 a can and golf balls at $1 each or tuna at $3 a can and golf balls at 50? ach? d. If Pete changes the quantities that he buys, which good will he buy more of and which less of? e. When the prices change next month, will there be an income effect and a substitution effect at work or just one of them? Solutions to Additional Problems 1. a. Marc’s real income is 4 cans of root beer. Marc’s real income in terms of cans of root beer is equal to his money income divided by the price of a can of root beer. Marc’s money income is $20, and the price of root beer is $5 a can. Marc’s real income is $20 divided by $5 a can of root beer, which is 4 cans of root beer. b. Marc’s real income is 2 CDs.

Marc’s real income in terms of CDs is equal to his money income divided by the price of a CD, which is $20 divided by $10 a CD or 2 CDs. c. The relative price of root beer is 1/2 CD. The relative price of root beer is the price of root beer divided by the price of a CD. The price of root beer is $5 a can and the price of a CD is $10, so the relative price of root beer is $5 a can divided by $10 a CD, which equals 1/2 CD per can. d. The opportunity cost of a can of root beer is 1/2 CD. The opportunity cost of a can of root beer is the quantity of CDs that must be forgone to obtain a can of root beer.

The price of root beer is $5 a can and the price of a CD is $10, so to buy one can of root beer Marc must forgo 1/2 CD. e. The equation that describes Marc’s budget line is QR = 4 – 2QCD. Call the price of a can of root beer PR and the quantity of root beer QR, the price of a CD PCD and the quantity of CDs QCD, and income y. Marc’s budget equation is PRQR + PCDQCD = y. If we substitute $5 for the price of a can of root beer, $10 for the price of a CD, and $20 for the income, the budget equation becomes $5QR + $10QCD = $20. Dividing both sides by $5 gives QR + 2QCD = 4.

Subtract 2QCD from both sides to give QR = 4 – 2QCD. f. To draw a graph of the budget line, plot the quantity of CDs on the x-axis and the quantity of root beer on the y-axis. The budget line is a straight line running from 4 cans on the y-axis to 2 CDs on the x-axis. g. The slope of the budget line, when CDs are plotted on the x-axis is (2. The magnitude of the slope is equal to the relative price of a CD. The slope of the budget line is “rise over run. ” If the quantity of CDs decreases from 2 to 0, the quantity of root beer increases from 0 to 4.

The rise is 4 and the run is (2. So the slope equals 4/(2, which is (2. 2. a. Marc buys 2 cans of root beer and 1 CD. Marc buys the quantities of root beer and CDs that moves him onto the highest indifference curve, given his income and the prices of root beer and CDs. The graph shows Marc’s indifference curves. So draw Marc’s budget line on the graph. The budget line is tangential to indifference curve I0 at 2 cans of root beer and 1 CD. The indifference curve I0 is the highest indifference curve that Marc can get attain. b. Marc’s marginal rate of substitution is 2.

The marginal rate of substitution is the magnitude of the slope of the indifference curve at Marc’s consumption point, which equals the magnitude of the slope of the budget line. The slope of Marc’s budget line is ? 2, so the marginal rate of substitution is 2. 3. a. Marc buys 1 can of root beer and 3 CDs. Draw the new budget line on the graph with Marc’s indifference curves. The budget line now runs from 4 CDs on the x-axis to 4 cans of root beer on the y-axis. The new budget line is tangential to indifference curve I1 at 1 can of root beer and 3 CDs.

The indifference curve I1 is the highest indifference curve that Marc can now get attain. b. Two points on Marc’s demand curve for CDs are the following: At $10 a CD, Marc buys 1 CD. At $5 a CD, Marc buys 3 CDs. c. The substitution effect is 1 CD. To divide the price effect into a substitution effect and an income effect, take enough income away from Marc and gradually move his new budget line back toward the origin until it just touches Marc’s indifference curve I0. The point at which this budget line just touches indifference curve I0 is 2 CDs and 0. 5 can of root beer.

The substitution effect is the increase in the quantity of CDs from 1 CD to 2 CDs along the indifference curve I0. The substitution effect is 1 CD. d. The income effect is 1 CD. The income effect is the change in the quantity of CDs from the price effect minus the change from the substitution effect. The price effect is 2 CDs (3 CDs minus the initial 1 CD). The substitution effect is an increase in the quantity of CDs from 1 CD to 2 CDs. So the income effect is 1 CD. e. CDs are a normal good for Marc because the income effect is positive. 4. a. Pete can still buy 20 cans of tuna and 40 golf balls.

When Pete buys 20 cans of tuna at $2 a can and 40 golf balls at $1 each, he spends $80 a month. Now that the price of a can of tuna is $3 and the price of a golf ball is $0. 50, 20 cans of tuna and 40 golf balls will cost $80. So Pete can still buy 20 cans of tuna and 40 golf balls. b. Pete will not want to buy 20 cans of tuna and 40 golf balls because the marginal rate of substitution does not equal the relative price of the goods. Pete will move to a point on the highest indifference curve possible where the marginal rate of substitution equals the relative price. c.

Pete prefers tuna at $3 a can and golf balls at $0. 50 each because he can get onto a higher indifference curve than when tuna is $2 a can and golf balls are $1 each. d. Pete will buy more golf balls and fewer cans of tuna. The new budget line and the old budget line pass through the point at 20 cans of tuna and 40 golf balls. If cans of tuna are plotted on the x-axis, the marginal rate of substitution at this point on Pete’s indifference curve is equal to the relative price of a can of tuna at the original prices, which is 2. The new relative price of a can of tuna is $3/50 cents, which is 6.

That is, the budget line is steeper than the indifference curve at 20 cans of tuna and 40 golf balls. Pete will buy more golf balls and fewer cans of tuna. e. There will be a substitution effect and an income effect. A substitution effect arises when the relative price changes and the consumer moves along the same indifference curve to a new point where the marginal rate of substitution equals the new relative price. An income effect arises when the consumer moves from one indifference curve to another, keeping the relative price constant.

Cite this Household’s Budget Line

Household’s Budget Line. (2016, Sep 15). Retrieved from https://graduateway.com/households-budget-line/

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