Exam 4: A Model of Production

If MPK = r, the firm:

In the year 2007, the five richest countries had a per capita GDP ________ times higher than the five poorest countries. Differences in capital per worker explain about ________ percent of this difference, with total factor productivity making up about ________ percent of this difference.

Refer to the following table when answering Table 4.1: Production Model's Prediction for Per Capita GDP (US = 1) Fredicted output Observed per capita, y= per capita GDP Switzerl and 0.966 1.083 United Kingdom 0.828 0.876 Japan 0.760 1.056 Italy 0.686 0.975 Spain 0.661 0.944 Brazil 0.201 0.559 South Africa 0.182 0.546 China 0.172 0.528 India 0.084 0.394 Burundi 0.010 0.180 -One explanation for the difference between the predicted output per person and the observed per capita GDP in Table 4.1 is differences in:

In the Cobb-Douglas production function $Y = K ^ { a } L ^ { b }$ , what do a < 1 and b = 1 - a reflect? Show how you derive your answer.

In the Cobb-Douglas production function $Y = \bar { A } K ^ { a } L ^ { 1 - a }$ , defining y = Y/L as output per person and k = K/L as capital per person, the per person production function is:

Differences in output across economies with the same per capita capital stock can be explained by:

In the Cobb-Douglas production function $Y = K ^ { a } L ^ { 1 - a }$ , the $\alpha$ represents:

Figure 4.5: Production Function -Consider the three production functions in Figure 4.5. Each represents a different country. For any given per capita stock of physical capital, which country has the highest total factor productivity?

A production function of the form $Y = K ^ { 2 } L ^ { 1 - a }$ is called the Cobb-Douglas production function.

The production function of the form $Y = K ^ { 1 / 3 } L ^ { 1 / 3 }$ exhibits constant returns to scale.

If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation $\bar { A } = y / k ^ { 1 / 3 }$ , if capital's share of GDP is one-third.

If MPL < w, the firm:

In the Cobb-Douglas production function $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ , labor's share of GDP is:

Figure 4.3: The Production Function -Consider Figure 4.3. The shape of this production function suggests:

The equation MPK = r* yields:

If the production function is given by $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ and K = 27 and L = 8, total output equals:

The marginal product of the labor curve represents the labor supply curve.

Write down the firm's profit maximizing problem. Be sure to identify the variables the firm can choose and which it takes as given. What should the firm facing the following scenarios do? • If the marginal product of capital is greater than the rental price of capital. • If the marginal product of labor is less than the wage.

A production function of the form $Y = K ^ { 2 } L ^ { 1 - a }$ exhibits constant returns to scale.

The marginal product of labor is measured in: