Ch. 4

We cannot tell whether the production function Y = KaL 1-a has constant returns to scale, because we do not know the value of a. T/F

F The Cobb-Douglas production function has constant returns to scale because the exponents a + (1-a) sum to 1.

If the marginal product of capital is less than the rental rate of capital, the firm should rent more capital. T/F

F A firm should only rent more capital if the MPK is greater than the rental rate of capital

The standard replication argument implies that Italy can raise its per capita GDP by doubling the amount of capital per person. T/F

F Capital per person is subject to diminishing returns to capital. Thus, because the exponent on capital per person is less than 1, doubling only the amount of capital per person will not double per capita output.

You plot the production function for the United States on a graph with output per person on the vertical axis and capital per person on the horizontal axis. If a shock occurs causing the productivity parameter to increase, the production function would shift upward. T/F

T A higher productivity parameter implies that U.S. production (output per person) is higher for any given level of capital per person

A production function has inputs X, Y, and Z and a productivity parameter . The production function A^(1/3)*X^(1/3)*Y^(1/3)*Z^(1/3) exhibits a. constant returns to scale. b. decreasing returns to scale. c. diminishing returns to scale. d. increasing returns to scale

a. constant returns to scale. Doubling each input X, Y, and Z, will result in a doubling of output. If the exponents on the inputs sum to 1, it has constant returns to scale.

Output per capita and output per worker are a. always equal. b. equal in the production model, but output per capita is smaller in general. c. equal in general, but output per capita is smaller in the production model. d. are not equal, because output per capita is always greater

b. equal in the production model, but output per capita is smaller in general. Note that in the production model output per capita and output per worker are equal, but this need not be the case in all models. Given that you cannot have more laborers in an economy than its population, output per capita is smaller than output per worker.

Consider a perfectly competitive economy with a production function Y = Abar*K^(1/3)*L^(2/3). There are 27 workers who produce cream cheese (a numéraire good) with 125 units of capital. If the productivity parameter is equal to 1 and the economyproduces 40 tons of cream cheese in equilibrium, what is the sum of the total payments to capital and labor? a. Cannot be determined because we don't know the wage rate and the rental rate of capital b. 152 tons of cream cheese c. 40 tons of cream cheese d. $40

c. 40 tons of cream cheese Since the numéraire good is cream cheese, all prices are expressed in tons of cream cheese. Total payments to capital and labor (w*L + r*K) are also expressed in tons of cream cheese. In equilibrium the sum of payments to capital and labor is equal to total production.

Consider an economy characterized by the production function Y = Abar*K^(1/2)*L^(1/2) where the productivity parameter is equal to 1.2. How many units of output can be produced with 25 units of capital and 64 workers? a. 10 b. 24 c. 48 d. 1,600

c. 48 A production function is a mathematical representation of the relationship between inputs and output, i.e. how much output can be produced with any input combination. Replacing Abar = 1.2, K = 25, and L = 64 yields Y = 48.

Output per person is higher when a. a country is more efficient in adopting a technology. b. a country has a higher capital-to-population ratio. c. a country has stronger property rights and contract enforcement. d. All of these choices are correct.

d. All of these choices are correct. A country has higher per capita output if capital per person and the productivity parameter are higher. The productivity parameter is higher under better institutions and when technologies are adopted more efficiently