Where It Comes From and Where It Goes Questions for Review 1 . The factors of production and the production technology determine the amount of output an economy can produce. The factors of production are the inputs used to produce goods and services: the most important factors are capital and labor. The production technology determines how much output can be produced from any given amounts Of these inputs. An increase in one of the factors of production or an improvement in technology leads to an increase in the economy’s output.
When a firm decides how much of a actor of production to hire or demand, it considers how this decision affects profits. For example, hiring an extra unit of labor increases output and therefore increases revenue; the firm compares this additional revenue to the additional cost from the higher wage bill. The additional revenue the firm receives depends on the marginal product of labor (MIL) and the price of the good produced (P).
An additional unit of labor produces MIL units of additional output, which sells for P dollars per unit. Therefore, the additional revenue to the firm is P x MIL.
The cost of hiring the additional unit of labor is he wage W. Thus, this hiring decision has the following effect on profits: Profit = Laurence – Accost = (p x MIL)- W. If the additional revenue, P x MIL, exceeds the cost (W) of hiring the additional unit of labor, then profit increases. The firm will hire labor until it is no longer profitable to do so-?that is, until the MIL falls to the point where the change in profit is zero. In the equation above, the firm hires labor until Profit = O, which is when (P x MIL) = W. This condition can be rewritten as: MIL = W/P.
Therefore, a competitive profit-maximizing firm hires labor until the marginal reduce of labor equals the real wage. The same logic applies to the firm’s decision regarding how much capital to hire: the firm will hire capital until the marginal product of capital equals the real rental price. 3. A production function has constant returns to scale if an equal percentage increase in all factors of production causes an increase in output of the same percentage. For example, if a firm increases its use of capital and labor by 50 percent, and output increases by 50 percent, then the production function has constant returns to scale.
If the production function has constant returns o scale, then total income (or equivalently, total output) in an economy of competitive profit-maximizing firms is divided between the return to labor, MIL x L, and the return to capital, MSP x K. That is, under constant returns to scale, economic profit is zero. 4. A Cob-Douglas production function function has the form F(K,L) = Kale-?a. The text showed that the parameter a gives capital’s share of income. (Since income equals output for the overall economy, it is also capital’s share of output. ) So if capital earns nonferrous of total income, then a = 0. 5. Hence, = AKA. LOL. 75. 5. Consumption upends positively on disposable income-?the amount of income after all taxes have been paid. The higher disposable income is, the greater consumption is. The quantity of investment goods demanded depends negatively on the real interest rate. For an investment to be profitable, its return must be greater than its cost. Because the real interest rate measures the cost of funds, a higher real interest rate makes it more costly to invest, so the demand for investment goods falls. 11 12 Answers to Textbook Questions and problems 6.
Government purchases are a measure of the dollar value of goods and revise purchased directly by the government. For example, the government buys missiles and tanks, builds roads, and provides services such as air traffic control. All of these activities are part of GAP. Transfer payments are government payments to individuals that are not in exchange for goods or services. They are the opposite of taxes: taxes reduce household disposable income, whereas transfer payments increase it. Examples of transfer payments include Social Security payments to the elderly, unemployment insurance, and veterans’ benefits. . Consumption, investment, and government purchases determine demand or the economy’s output, whereas the factors of production and the production function determine the supply of output. The real interest rate adjusts to ensure that the demand for the economy’s goods equals the supply. At the equilibrium interest rate, the demand for goods and services equals the supply. 8. When the government increases taxes, disposable income falls, and therefore consumption falls as well. The decrease in consumption equals the amount that taxes increase multiplied by the marginal propensity to consume (MAC).
The higher the MAC is, the greater is the negative effect of the tax increase on consumption. Because output is fixed by the factors of production and the production technology, and government purchases have not changed, the decrease in consumption must be offset by an increase in investment. For investment to rise, the real interest rate must fall. Therefore, a tax increase leads to a decrease in consumption, an increase in investment, and a fall in the real interest rate. Problems and Applications b. To find the amount of output produced, substitute the given values for labor and land into the production function: Y = 1000. 1000. 5 100. According to the text, the formulas for the marginal product of labor and the original product of capital (land) are: MIL = (1 – a)Kcal-a d. ILL -a In this problem, a is 0. 5 and A is 1 . Substitute in the given values for labor and land to find the marginal product of labor is 0. 5 and marginal product of capital (land) is 0. 5. We know that the real wage equals the marginal product of labor and the real rental price of land equals the marginal product of capital (land). Labors share of the output is given by the marginal product of labor times the quantity of labor, or 50.
The new level of output is 70. 71. The new wage is 0. 71 . The new rental price of land is 0. 35. Labor now receives 71 . . A production function has decreasing returns to scale if an equal percentage increase in all factors of production leads to a smaller percentage increase in output. For example, if we double the amounts of capital and labor, and output less than doubles, then the production function has decreasing returns to scale. This may happen if there is a fixed factor such as land in the production function, and this fixed factor becomes scarce as the economy grows larger.
A production function has increasing returns to scale if an equal percentage increase in all factors of production leads to a larger percentage increase in output. For example, if doubling inputs of capital and labor more than doubles output, then the production function has increasing returns to scale. This may happen if specialization of labor becomes greater as the population grows. For example, if only one worker builds Chapter 3 National Income: Where It Comes From and Where It Goes 13 a car, then it takes him a long time because he has to learn many different skills, and he must constantly change tasks and tools.
But if many workers build a car, then each one can specialize in a particular task and become very fast at it. 3. A. G. According to the neoclassical theory of distribution, the real wage equals the marginal product of labor. Because of diminishing returns to labor, an increase in the labor force causes the marginal product of labor to fall. Hence, the real wage falls. Given a Cob-Douglas production function, the increase in the labor force will increase the marginal product of capital and will increase the real rental price of capital. With more workers, the capital will be used more intensively and will be more productive.
The real rental price equals the marginal product of capital. If an earthquake estrous some of the capital stock (yet miraculously does not kill anyone and lower the labor force), the marginal product of capital rises and, hence, the real rental price rises. Given a Cob-Douglas production function, the decrease in the capital stock will decrease the marginal product of labor and will decrease the real wage. With less capital, each worker becomes less productive. If a technological advance improves the production function, this is likely to increase the marginal products of both capital and labor.
Hence, the real wage and the real rental price both increase. High inflation that doubles the nominal wage and the price level will have no impact on the real wage. Similarly, high inflation that doubles the nominal rental price of capital and the price level will have no impact on the real rental price of capital. According to the neoclassical theory, technical progress that increases the marginal product of farmers causes their real wage to rise. The real wage for farmers is measured as units of farm output per worker. The real wage is W/IF, and this is equal to ($/worker)/($/unit of farm output).
If the marginal productivity of barbers is unchanged, then their real wage is unchanged. The real wage for barbers is measured as haircuts per worker. The real wage is W/BP, and this is equal to ($/worker)/($/haircut). If workers can move freely between being farmers and being barbers, then they must be paid the same wage W in each sector. If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods.
We know that W/P = MIL so that W = p x MIL. This means that PIMPLE = BPML, given that the nominal wages are the same. Since the marginal product of labor for barbers has not changed and the marginal product of labor for farmers has risen, the price of a haircut must have risen relative to the price of the farm output. If we put it in growth-rate terms, then the growth of the farm price + the growth of the marginal product of the farm labor -? the growth of the haircut price. Both groups benefit from tech analogical progress in farming.
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