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Questions and Answers on Demand Estimation

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DEMAND THEORY 1a) The demand curve for haircuts at Terry Bernard’s Hair Design is P = 15 – 0. 15Q where Q is the number of cuts per week and P is the price of a haircut. Terry is considering raising her price above the current price of RM9. Terry is unwilling to raise price of the price hike will cause revenue to fall. Should Terry raise the price of haircuts above RM9? Why or why not? b) Terry is trying to decide on the number of people to employ based on the following short-run production function: Q = 12L – 0.

5L2 Where Q is the number of cuts per week and L is the number of workers.

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Suppose the price of a haircut is RM9, how many people should be hired if she pays each worker RM60 per week. 2. Based on a consulting economist report, the demand function for Formula 1 stickers by two individuals, (assuming the market has only 2 individuals) Q1 = 16 – 4PQ2 = 20 –2P respectively a.

What is the market demand curve equation? Write it in the conventional way. b. Given the total cost as TC = 2 + 0. 9Q2. Calculate the profit maximizing quantity and price and the total profits. c. Draw a diagram showing the equilibrium situation in (b). 3.

The market demand and supply functions for a consumer item are as follow: Qd = 120 – 6P Qs = 20 +4P a) Determine the equilibrium price and quantity. b) If the government sets a minimum price of $12 per unit, how many units would be supplied and how many units would be demanded? c) If demand increases to : Qd’ = 200 – 6P, determine the new equilibrium price and quantity. d) Draw a figure showing equilibrium price and quantity as in part (a) and part (c). 4. Zaid’s Frozen Pizza have enjoyed rapid growth in West Malaysia. From the analysis, it was found that the demand curve follows this pattern

Q = 1,000 – 3,000P + 10A Where, Q = Quantity demanded P = Product Price (in RM) A = Advertising expenditure (in RM) a. Assume that P = 3 and A = 2,000. Suppose the firm reduces price. Would this increase total revenue? Explain. b. Assume that P = 4 and A = 2,100. Suppose the firm reduces price. Would this increase total revenue? Explain. 5. Given the following supply and demand equations Qd = 102 – 6P Qs = 11 + 6P a. Determine the equilibrium price and quantity. b. If the government sets a minimum price of $9 per unit, how many units would be supplied and how many would be demanded? c.

If the government sets a maximum price of $5 per unit, how many units would be supplied and how many would be demanded? d. If demand increases to Q’d = 200 – 5P, determine the new equilibrium price and quantity. 6. The Rosenburg Corporation, a maker of machine tools, determines that the demand curve for its products is as follows: P = 1,000 – 40Q Where P is the price (in dollars) of a machine tool, and Q is the number of machine tools sold per month. a. What is the price elasticity of demand if price equals $500? b. At what price, if any, will demand for Rosenburg’s product be of unitary elasticity? . Using the above equation, determine the output rate that maximizes total revenue of Rosenburg’s Corporation? d. Illustrate your answer using TR, AR and MR functions showing various degrees of elasticities. 7. David & Sons Co. Ltd producing standard steel bars has following demand curve: P = 2000 – 20Q Where P is the price, and Q is the number sold per month. a. Derive the marginal revenue curve for the firm. b. At what output is the demand for the firm’s product price elastic? c. If the firm wants to maximize its dollar sales volume, what price should it charge? 8.

Eye-de-ho Potatoes is a product of the Coeur d’ Alene Growers’ Association. Producers in the area are able to switch back and forth between potato and wheat production depending upon market conditions. Similarly, consumers tend to regard potatoes and wheat (bread and bakery products) as substitutes. As a result the demand and supply of Eye-de-ho Potatoes are highly sensitive to changes in both potato and wheat prices. Demand and supply functions for Eye-de-ho Potatoes are as follows: Qd = -1,450 – 25P + 12. 5Pw + 0. 2Y———– Demand Qs = -100 + 75P – 25Pw – 12. PL + 10R———– Supply Where P is the average wholesale price of Eye-de-ho Potatoes ($ per bushel), Pw is the average wholesale price of wheat ($ per bushel), Y is income (GNP in $ billions), PL is the average price of unskilled labor ($ per hour), and R is the average rainfall ( in inches) Both Qd and Qs are in millions of bushels of potatoes. a. When quantity is expressed as a function of price, what are the Eye-de-ho Potatoes demand and supply curves if P = $2, Pw = $4, Y = $7,500 billion, PL = $8, and R = 20 inches? b.

Calculate the surplus or shortage of Eye-de-ho Potatoes when P = $1. 5, $2, and $2. 50. c. Calculate the market equilibrium price/ output combination. 9. The following relations decribe monthly demand and supply relations for dry cleaning services in the metropolitan area: Qd = 500,000 – 50,000P———-Demand Qs = -100,000 + 100,000P ———- Supply Where Q is quantity measured by the number of items dry cleaned per month and P is average price in dollars. a. At what average price level would demand equal zero? b. At what average price level would supply equal zero? c.

Calculate the equilibrium price/ output combination. 10. The Creative Publishing Company (CPC) is a coupon book publisher with markets in several southeastern states. CPC coupon books are either sold directly to the public, sold through religious and other charitable organizations, or given away as promotional items. Operating experience during the past year suggests the following demand function for CPC’s coupon books: Q = 5000 – 4000P + 0. 02Pop + 0. 5I + 1. 5A, Where Q is quantity, P is price($), Pop is population, I is disposable income per household ($), and A is advertising expenditures ($) . Determine the demand faced by CPC in a typical market in which P = $10, Pop = 1,000,000 persons, I = $30,000, and A = $10,000. b. Calculate the level of demand if CPC increases annual advertising expenditures from $10,000 to $15,000. c. Calculate the demand curves faced by CPC in Parts (a) and (b). 11. The demand curve for a hair cut at Lucky Star Hair Saloon is estimated to be P = 30 – 0. 2Q Where Q is the number of hair cut and P is the price per hair cut Current price level is RM10 for a hair cut. a. Calculate the price elasticity for hair cut at Lucky Star Hair Saloon at the given price. b.

Should Lucky Star Saloon raise the current price to increase its total revenue? Why or why not? TUTORIAL 2:DEMAND ESTIMATION 1. A study was done to look at demand for ‘Mar and Mas’ cheese cake. A regression analysis was conducted using the following model. Q = a + b1P + b2A + b3Y + b4H + b5 Pc Where Q = Quantity demanded in hundreds P = Price in RM (55) A = Advertising expenditures, in thousands (20) Y = Average household income, in thousands (31) H = Total number of residential sales, in thousands (10) Pc = Price of leading competitor, in RM (50) Values in parentheses are the assumed values.

Data were collected over 16 quarters. The results of the computer analysis are shown below. |Variable |Coefficient |Std Error |t-statistic | |Intercept |40 |2. 5 |16 | |P |-1. 1 |0. 9 |-1. 22 | |A |1. 5 |0. 6 |2. 5 | |Y |0. 2 |0. 12 |2. 67 | |H |0. 5 |0. 17 |2. 94 | |Pc |0. 1 |0. 75 |0. 13 | Coefficient of determination = 0. 91 Standard error of estimate = 2. 8 F-value= 311. 43 a. Write down the estimated regression equation. Using the assumed values, estimate quantity demanded. b. How concerned should this company be about price discounts by its leading competitor?

Explain. c. Should this company consider discounting its price in order to increase total revenue? Explain. d. How effective do you think advertising is for this company? e. What type of good is ‘Mar and Mas’ cheese cake? f. Describe the statistical significance of each individual independent variable included in the model. Given the t-value at 95% confidence interval as 1. 96. g. Comment on the coefficient of determination and F values. Can this estimated regression equation be accepted? h. Indicate the 95% confidence interval of the range of forecasted demand and the range of total revenue for cheese cake. 2.

Fukaku Footwear wished to estimate the demand function for its ‘Elite VS600’ women’s shoes. The company’s economist believed that the main determinants of ‘Elite VS600’ shoes are: i) the price of the shoes (Px) ii) the price of a competitor’s shoes Dr. Martin (Py) iii) the price of another competitor’s shoes ‘Madame69’ (Pz) and iv) disposable per capita income (Y) A regression was run by using SPSS package and the result is shown as follows: LS//Dependent Variable is Qx |Variable |Coefficient |Standard Error |t-statistic | |C |250. |- |- | |Px |-410. 3 |-150. 3 |2. 73 | |Py |240. 3 |180. 5 |1. 33 | |Pz |180. 3 |70. 4 |2. 56 | |Y |1. 23 |0. 23 |5. 36 | R-Squared = 0. 857 S. E of regression = 265. Qx represents quantity (pairs) demanded per month. The current values of the dependent variables are Px = $80, Py = $75, Pz $82. 5 and Y = $5250 a) Calculate the price and income elasticities of demand for ‘Elite VS600’ shoes. What do these values mean? b) Derive the equation of the demand curve and write it in the conventional way. c) Suppose that the marginal cost of Elite VS600 is constant at $50, what is the profit maximizing price and output? d) At the profit maximizing price, what range of sales volume can be expected at 95% confidence limits? e) Do you accept or reject the above regression results? Explain. 3.

The economist in the Copper Industry estimated the world demand for copper using ordinary least-square method (Qo = a + bPc + cM + dPA). The estimated results are as follows. Dependent Variable:QcR-SquareF-RatioP-Value on F Observations:250. 9646190. 8460. 0001 |Variable |Coefficient Estimate |Standard Error |T-ratio |P-value | |Intercept |-6150. 039 |931. 024 |-6. 60 |0. 0001 | |Pc |-12. 517 |14. 37 |-0. 87 |0. 3936 | |M |12065. 0 |720. 48 |16. 74 |0. 0001 | |PA |65. 379 |29. 782 |2. 20 |0. 0395 | Where Qc=World consumption (sales) of copper in 1000’s of metric tons Pc=Price of copper in cents per pound M=Index of real per capita income PA=Price of aluminum in cents per pound Answer the following questions: a. Do the coefficient estimates for b, c and d in the model have the expected sign? Explain. b. Which of the coefficient estimates are statistically significant at the 5 percent level of significance? . Form the demand function based on the above table. d. Using the values Pc = 33. 90, M = 0. 70, PA = 23. 93 Derive the demand curve function. Calculate the following elasticities of demand. i) The price elasticity of demand ii) The cross elasticity of demand iii) The income elasticity of demand e. Using the estimates in (d), evaluate the world consumption of copper of: i) The formation of a worldwide cartel in copper that increases the price of copper by 10%. ii) The onset of a recession that reduces world income by 5 %. iii) A technical breakthrough that is expected to reduce the price of copper by 6%. v) A 10% reduction in the price of aluminum. 4. Khalid & Company has commissioned a study to quantify the determinants of the demand for its speed control device (x). This device is installed in an automobile to allow the vehicle to maintain a constant speed, with subsequent fuel economy advantage. Based on the data available from sources, a consultant firm has estimated the following regression equation. Qx = 125. 0 – 18. 62Px + 12. 26Py + 5. 24Ax + 28. 60Y (2. 57) (2. 55)(4. 94) (15. 24) R2 = 0. 82 Standard error of estimate = 12. 43 Where:Qx = quantity demanded of x (unit/month) Px = Price per unit of x (in RM)

Py = Price of the competitor (in RM) Ax = X’s advertising budget per month (RM’000) Y = Per capita income per month (RM’000) The figures in the parentheses show the t-values a. Interpret the meaning of the coefficients of independent variables, the coefficients of determination and what can you say about the estimated regression equation? b. Given Px = $20, Py = $21, Ax = 14. 5 and Y = 1. 25 Calculate and interpret the price elasticity and advertising elasticity of demand for the product. c. If the marginal cost of production is constant at $12 per unit, at what price will the profit be maximised? d.

At the profit-maximizing price, in what range of output figures do you expect to fall at 95% confidence level? 5. Deck & Blacker is a maker of small kitchen appliances. Its economist estimates the following demand for its toaster ovens: Q = 40 – 1. 1P + 1. 5A + 0. 32Y + 0. 5H + 0. 1Pc (1. 22) (2. 5) (2. 67) (2. 94) (0. 13) R2 = 0. 91 SEE (standard error of estimation) = 2. 8 Where: Q is quantity demanded of toaster ovens in thousands P is price of toaster ovens in RM A is advertising expenditure in thousands Y is average household income in thousands H is total number of residential sales in thousands

Pc is price of competitor’s brand in RM And figures in parentheses show the t-values for each coefficient. Given also P = 55, A = 20, Y = 31, H = 10, Pc = 50 a. Which coefficients are statistically significant at the 5% level or 95% confidence interval? (Given the tabled t-value is 1. 96) Interpret the coefficient of determination R2. b. Calculate income elasticity of demand. Is the toaster oven a luxury good or a necessity? c. What impact would a 1% increase in competitor’s price have on the quantity demanded of Deck & Blacker’s toaster ovens? d. Assess the impact of advertising on quantity demanded. e.

Should this company consider discounting its price in order to increase its total revenue? Explain. f. Derive an expression for the firm’s demand curve for toaster ovens. g. If the firm’s objective is to maximise total revenue from the sales of toaster ovens, at what price should the firm charge? h. At that price, what range of sales volume can be expected at the 95% confidence limits? 6. Sharp Edge Inc. (SEI) is a producer of Polo Knives, a set of kitchen cutlery, which it markets on a nationwide basis. Their knife sets are either sold directly to the public through national television marketing programs, or given away as promotional items.

Operating experience during the past year suggest the following demand function for its knife sets: Q=4,000 – 4,000P + 10000N + 0. 5Y + 0. 4A (1010) (3140) (0. 22)(0. 14) R2=0. 83 SEE=283 The value in the parenthesis is the standard error of coefficient. Q is quantity, P is the price(RM). N is the average Neilson rating of television programs during which the company advertise their knives. Y is average disposable income per household (RM) and A is advertising expenditures (RM). The current values of the variables are P = 35, N = 18. 5, Y = 22,000 and A = 500,000 . Determine the demand curve equation faced by SEI in a typical market. State the demand curve equation with quantity expressed as a function of price, and with price expressed as a function of quantity. b. Calculate the price necessary to sell 264,000 and 320,000 sets of knives. c. Do you agree that a price increase will increase the total revenue of the company? d. Calculate the income elasticity. What is the impact on demand during periods of recession? e. Which of the independent variables are statistically significant at 95% confidence interval in explaining the quantity change? Use the rule of thumb = 2) f. Is the regression acceptable? Explain your answer. g. Based on 95% confidence interval, compute the range of quantity demanded at the total revenue-maximizing price. TUTORIAL 3:PRODUCTION THEORY 1. The Tiny Tots company employs machines and workers to produce toys. The production function is given by: Q = 20K 0. 5 L 0. 5 Input prices are RM100 for machines and RM20 for labour. The firm is currently using 121 units of labour and 36 machines. a. How much output is the firm producing with these inputs? b. Could the firm produce this same level of output more efficiently?

Explain. c. What is the expansion path for this production function? d. What should be the optimal combination of capital and labour to produce the present output level? e. Calculate the total cost of production for this optimal output. 2. Syarikat Kemajuan is an electrical firm which specializes in producing bulbs. It produces these bulbs according to the following short-run production function. Q = K (5L – 1. 25L2) Where Q is the quantity of bulbs in units produced per week. L is labour in units and K is machinery used in units which is fixed at 2. The wage rate of labour and price of capital is RM50.

The company has received an order from a contractor for 10 bulbs at the market price of RM20 per unit. a. Determine the optimal rate of labour used. b. At the optimal combination of inputs should the company accept this offer? Explain your answer. 3. Matahari Enterprise deals in furniture. Its production function (Q) is given as Q = 2K 1. 6 L 1. 2 Input prices are RM15 for (K) capital and RM10 for (L) labour. The firm is currently using 20 units of labour and 40 units of machines. a. Calculate the marginal product of labour and marginal product of capital at the given input rates. b.

What is the equation for the expansion path? Calculate the total cost of production. c. Is the current input mix efficient? If not, calculate the efficient input mix, based on the total cost calculated in (b). d. Calculate the total quantity produced using the efficient input mix. Using the isoquant-isocost diagram show the efficient mix. (label your diagram). Determine the return to scale of the production function above and interpret it. 4. A firm specializing in the production of calendars has the following production function. Q = 12 L 0. 45 K 0. 30 Where Q = output, L = Labor input, K = capital input

Per unit price of labour is $10 and capital is $8. The total cost is $1000. a. Derive the Constraint and Lagrangian function. b. Determine the optimal combination of labor and capital. Check if the optimal condition is satisfied for the solution obtain above. c. What is the value of the Lagrangian multiplier and interprete its meaning. d. Calculate: i. the maximum output that can be produced using the optimal combination of output. ii. the average cost per unit of output. e. Determine the percentage increase in output if both labor and capital are each increased by 20%. 5. a.

For each of the following production functions, determine whether returns to scale are decreasing, constant, or increasing. K and L are capital and labour inputs. i. Q = K + 0. 5L + KL ii. Q = 40K 0. 7 L 0. 6 iii. Q = 300 + 4K + 3L iv. Q = 5K/5L b. The total revenue (TR) function for a firm is given by: TR = 2,000Q – 10Q2 Where Q is the rate of output per period. Determine the rate of output that results in maximum total revenue. (Be sure that you have maximized, not minimixed, total revenue) 5. Diha Manufacturing employs machinists and gear-making machines to produce gears.

The production function is given by: Q = 10K 0. 8 L 0. 2 Input prices are RM200 for machines and RM10 for labor. The firm is currently using 200 units of labor and 40 machines. a. What are the marginal products of labor and capital at the rates of input use specified? b. Is the current input mix efficient? Explain. If not, how should it be changed? c. Find the expansion path. 6. Muadz Corporation producing tiles has the following short-run production function. Q = 50L + 6L2 – 0. 5L3 Where Q = Quantity of output per week L = Labor (number of workers) i. When does the law of diminishing returns take effect? ii.

Calculate the range of values for labor over stages I, II and III of production. iii. Assume each worker is paid RM400 per week. How many workers should the firm hire if the price of the output is RM10? 7. The production function of Syarikat Triple-A is given by: Q=0. 5LK – 0. 1L2 – 0. 05K2 Where Q=units of output K=units of capital=8 units L=units of labor=15 units r=price of capital=RM25 per hour w=price of labor=RM20 per hour a. Calculate the total cost and derive the Langrangian Function b. How can the production manager change the input mix to achieve a higher level of output given the current total cost? 8.

Ming Tai Plastics Bhd. which produces plastic pails has estimated its production function to be as follows: Q=20K 0. 7 L 0. 5 WhereQ=rate of output K=capital input L=labor input It currently pays RM200 for each unit of capital and RM20 for each unit of labour. Ming Tai Plastics Bhd. currently employs 5 units of capital and 100 units of labor. a. Determine the current output level. b. Explain what is an expansion path and use a diagram to illustrate. c. Derive the expansion path equation for Ming Tai Plastics Bhd. d. What should be the optimal combination of capital and labour to produce the present level of output? . Compare the average cost per unit of output using the current input mix and the optimal input mix. f. Determine whether the production function exhibit constant, increasing or decreasing returns to scale? Explain. g. Determine the percentage increase in output if both labor and capital are each increased by 15%. TUTORIAL 4:COST CONCEPTS 1. A chemical firm that causes serious water pollution has fixed cost of 500 and variable cost of 200Q + 0. 4Q2 – 0. 06Q3. The external cost is 100 + 50Q + 0. 2Q2 Q = amount of crates (millions) of chemical produced per period a. Determine the total cost function. . What is the shut-down price? c. What is the cost of pollution for an output of 10 millions crates per period. d. Suggest a fine per unit of output if the firm produces 10 million crates per period. 2. A firm produces its product on two assembly lines and operates with the following total cost function: TC = 3×2 + 6y2 – xy Where x and y stand for two different products. The above function is subject to the constraint that the total output of the product is 20 units. a. Formulate the langrangian function and determine the output levels of the two products that will minimize the firm’s cost. b.

Find the value of ( (lagrangian multiplier) and interpret it. 3. The demand and cost function for a company are estimated to be as follows. P =100 – 8Q TC=50 + 80Q – 10Q2 + Q3 Where P=Price Q=Output TC=Total Cost a. What price should the company charge if it wishes to maximize its profit in the short-run? b. What price would it charge if it wishes to maximize its revenue in the short-run? 4. NR company manufactures buttons (B) and zippers (Z). Its production department estimates that the average-cost function of the firm is AC = B2 + 2Z2 – 2BZ – 2B – 6Z + 20 The firm expects an order of both goods that will require it to produce total output of 6 units. i. Using the Lagrangian method, find the level of output of button and zipper at which the firm minimizes its average cost. Compute the Lagrangian multiplier. ii. Find the minimum average cost. iii. Determine the minimum average cost if the order on both goods require it to produce a total output of 7 units. 5. Hardwood Cutters offers seasoned, split fireplace logs to consumers in Kampong Parit, Perak. The company is the low-cost provider of firewood in this market with fixed costs of RM10,000 per year, plus variable costs of RM25 for each unit of firewood. Annual demand for the company is:

P=225 – 0. 125Q Where P is the price of firewood per unit and Q is the number of units of firewood a. Determine the marginal revenue and the marginal cost function. b. Calculate the profit maximizing quantity, price and profit. c. Calculate the price elasticity at the profit-maximizing price. 6. Home-Theater, Inc is a manufacturer and distributor of high-resolution 40-inch projector television for individual and commercial customers. Cost relations are : TC=2,000,000 + 1,500Q + 0. 5Q2 a. Determine the equations for the average variable cost, average cost and marginal cost function. b.

Calculate output at the average cost minimizing activity level. c. Is the firm producing in the short-run or long run? Explain your answer. TUTORIAL 5:THEORY OF FIRMS 1. The Watt Company is a member of the lamp industry which is perfectly competitive. The price of a lamp is RM25. The firm’s total cost function is: TC = 2000 + 10Q + 0. 02Q2 Where Q is output. a. What is the profit-maximising output of the firm? b. What is the firm’s economic profit at this output? c. What is the firm’s average cost at this output? d. If other firms in the lamp industry have the same cost function as this firm, is the industry in equilibrium in the long-run?

Why or why not? 2. Suppose that the manager of a firm operating in a perfectly competitive market has estimated the firm’s average variable cost function to be AVC = 10 – 3Q + 0. 5Q2 Where Q is output. Suppose that total fixed cost (TFC) is RM600. a. What is the corresponding marginal cost(MC) function? b. At what output is AVC at its minimum? c. What is the minimum value for AVC? d. In the short-run, if the market price for the firm’s product is RM5, should the firm continue or stop production? Why? 3. a. Explain the different degrees of price discrimination. b.

An amusement park, whose customer set is made up of 2 markets, adults and children, wants to charge different entry prices for adults and children. What conditions must exist before price discrimination of this nature can take place? 4. A firm in an oligopolistic industry has identified 2 sets of demand curves. If the firm is the only one that changes prices (that is, other firms do not follow), its demand curve take the form Q = 150 – 25P. If, however, it is expected that competitors will follow the price actions of the firm, then the demand curve is of the form Q = 66. 67 – 8. 3P. a. Calculate price and quantity at the kink. . Derive the marginal revenue functions of the 2 sets of demand curves. c. What is the range over which a marginal cost curve could rise or fall without affecting the price the firm charges? d. If the total cost function is TC = 2. 5 + 1. 5Q +0. 02Q2, is the quantity at the kink optimal? Explain. e. Draw a diagram to show the equilibrium position of this oligopolistic firm. 5. Suppose that the demand function for a product produced by a monopolist is given by the equation. Q = 6. 66 – 0. 33P The total cost of production is given by the equation TC = 2Q2 a. Find the profit maximizing output and price per unit. b.

Determine the monopolist’s profit at the profit maximizing output level. c. Compare the sales maximizing output with the profit maximizing output level calculated in (a) above. Is there any difference? Show your calculation. d. Compare total revenue at the sales maximizing and profit maximizing output levels. Is there any difference? Show your calculation. 6. Suppose that a firm selling exclusive jackets in two separate markets. The markets are allocated in Kelantan and Johore. The demand equation for the jackets in Kelantan is: Qk = 100 – Pk Johore is: Qj = 50 – 0. 25Pj The firm’s total cost function is TC = 150 + 5Q

If the firm engages in third-degree price discrimination a. How much should the firm sell in Kelantan and Johore? b. What price will the firm charge in each market? c. What will be the firm’s monthly profit? 7. During several past wars and more recently under programs designed to curb inflation the government has imposed price ceiling on certain commodities. This is done to keep prices from rising to the natural level that would prevail under supply and demand equilibrium. The result is that the quantity that sellers are willing to supply at the ceiling price often falls short of the quantity demanded at that price.

To bring supply and demand more into equilibrium, ration coupons are sometimes issued. a. If the aggregate demand curve for commodity X is P = 100 – 5Q, and the industry supply curve for that product is P = 10 + 10Q, calculate the following: j. The equilibrium price and quantity for commodity X. ii. The quantity that will be sold if the ceiling price of $60 is established. b. The market supply and demand for commodity X are the original equation used in the above problem (3a). The industry is perfectly competitive, and the marginal cost equation for one firm, Alisan & Co. is given by MC = 30 + 4Q i.

What is the short-run profit-maximizing output rate for Alisan & Co.? ii. Average cost is given by AC = 100 + 30 + 2Q Q In the short run, how much profit will the firm earn? c. Chilhan Motors Inc. faces a kinked demand curve with a demand equation P1 = 150 – 0. 5Q when quantity is less than 50 P2 = 200 – 1. 5Q when quantity is greater than 50 The firms total cost is TC = 500 + 60Q + 0. 1Q2 i. Determine the price and quantity at the kinked point. ii. What is the profit maximizing price and quantity? Show your working. 8. Global Metals, Inc (GMI) supplies standard electrical wiring to the construction and renovation markets.

The wire supply industry can be regarded as perfectly competitive. Total and marginal cost relations for the GMI are: TC = 3600 + 5Q + 0. 01Q2 MC = 5 + 0. 02Q Where Q is hundreds of feet of wire produced. i. Calculate GMI’s optimal output and profits if wire prices are stable at $20. ii. Calculate GMI’s optimal profits if wire prices rise to $25. iii. If GMI is typical of firms in the industry, calculate the firm’s equilibrium output, price and profit levels, in the long run. 9. A producer has the possibility of discriminating between domestic and foreign market for a product where the demand respectively is Q1 = 21 – 0. 1P1

Q2 = 50 – 0. 4P2 Total Cost = 2000 + 10Q where Q = Q1 + Q2. What price will the producer charge in order to maximize profits: a. with discrimination between markets b. without discrimination c. compare the profit differentials between discrimination and non discrimination d. what are the conditions for price discrimination? 10. Naim & Company use first-degree price discrimination in selling its product. Its demand function is given as P = 200 – 10Q and marginal cost is constant at RM10. There is no fixed cost. With first-degree price discrimination, what is the firm’s profit-maximizing output rate and the maximum profit? 1. Perak Steel faces a kinked demand curve. The demand equations are P1 = 600 – 0. 5Q1 and P2 = 700 – 0. 75Q2 a. If the firm’s marginal cost is RM150, what is the profit-maximizing quantity and price? b. If the firm’s new marginal cost is given as RM250, what will be the profit-maximizing quantity and price? c. Illustrate (a) and (b) on a separate graphs. d. Briefly explain any three(3) characteristics of the market structure faced by Perak Steel. 12. Syarikat Alpha Print, a perfectly competitive firm, supplies printing ink to offices. The total cost function of Syarikat Alpha Print is given as follows:

TC=2500 + 5Q + 0. 25Q2 a. Calculate Syarikat Alpha Print’s profit-maximizing output level if the market price of a bottle of printing ink is RM60. b. Explain the impact on profits of Syarikat Alpha Print if the market price of a bottle of printing ink increases to RM65. c. If all other firms in the industry have the same cost function, calculate the long-run equilibrium output and price. 13. Healthy Living Bhd. produces multivitamins for two distinct markets: private clinics and government clinics. Healthy Living Bhd. estimated the demand in each market to be as follows:

Private clinics:Qp=170 – 1. 9Pp Government Clinics:Qg=65 – 0. 45Pg Marginal cost of producing each bottle of multivitamins is constant at RM30 per bottle. a. If Healthy Living Bhd. practised price discrimination, what would be the price of each bottle of multivitamins for: i. private clinics? ii. Government clinics? b. If Healthy Living Bhd. practised a single price policy, what price would the firm charge? c. Would you advise Healthy Living Bhd. to practise price discrimination? d. Sketch a diagram to illustrate price and quantity in each of the markets.

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Questions and Answers on Demand Estimation. (2016, Nov 08). Retrieved from https://graduateway.com/demand-estimation-2/

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