Production Function & Solow Growth Model

Suppose India has a per capita GDP that is .074 times the United States GDP. It has a capital-per-person ratio that is .035 times that of the United States. Compared to the United States, the implied value of total factor productivity for India is approximately

.23 The United States is standardized to a value of 1 in this problem. The implied value of TFP is equal to the ratio of output per person divided by the capital-to-labor ratio raised to the 1/3 power.

Consider a perfectly competitive economy with a production function. 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 economy produces 40 tons of cream cheese in equilibrium, what is the sum of the total payments to capital and labor?

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 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?

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 K = 25, and L = 64 yields Y = 48.

A firm uses capital and labor to produce a good. Which of the following is greatest?

Accounting profit Economic profit equals total revenue minus payments to all inputs. Accounting profit equals total revenue minus payments to inputs other than capital.

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

False 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 double its per capita GDP by doubling the amount of capital per person.

False 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.

We cannot tell whether the production function Y = KaL1-a has constant returns to scale, because we do not know the value of a.

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

Capital per person explains about one-half of the difference in per capita income between the richest and poorest countries.

False The capital-to-population ratio explains about one-third of the difference, while TFP explains the rest.

Output per person is higher when

a country is more efficient in adopting a technology. a country has a higher capital-to-population ratio. a country has stronger property rights and contract enforcement. 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.

What is the marginal product of capital (MPK) for the production function

The marginal product of capital for a Cobb-Douglas production function is proportional to the average amount produced by each unit of capital where the factor of proportionality is equal to the exponent on capital.

In a Cobb-Douglas production function, the factor share of income going to each input is equal to the exponent on the input in the production function.

True Regardless of the amount of capital or labor in an economy, the exponents in the production function determine the factor shares.

According to Figure 4.5, does the production model accurately predict the level of per capita GDP for Singapore?

Yes, because the predicted value of per capita GDP for Singapore is close to the actual value of its per capita GDP

If the productivity parameter is assumed to equal 1, the production model

correctly identifies that countries are richer if they have more capital. incorrectly predicts that poor countries are substantially richer than they are. incorrectly predicts that some countries are richer than the United States. The model implies that more capital implies more output per person but incorrectly overestimates the value of per capita output.

In the Solow model, if investment is ________ depreciation, the capital stock ________.

greater than, grows

In the Solow model, net investment is defined as:

investment - capital depreciation

In the Solow model, the steady-state level of output per worker is a function of:

productivity, the depreciation rate, and the saving rate.

The steady state is defined as the point where capital accumulation, ΔKt, is equal to:

zero