economics beginner 10 sample questions

Production Theory MCQ Practice Test

Resource combination for outputs

Q1. A firm's production function exhibits increasing returns to scale. However, the marginal product of labor begins to decline after 10 units of labor are employed, holding other inputs constant. What is the likely cause of this phenomenon?

A. The law of diminishing marginal returns is not applicable in this case.
B. The firm's technology is not suited for large-scale production.
C. The firm is experiencing diseconomies of scale.
D. The law of diminishing marginal returns. ✓

Explanation: The marginal product of labor declines because, holding other inputs constant, each additional unit of labor has less capital and other inputs to work with. This is the law of diminishing marginal returns. Increasing returns to scale refers to the situation where all inputs are increased proportionally, leading to a more than proportional increase in output.

Q2. A firm is producing a good using two inputs, labor and capital. The production function is given by Q = 10L^0.4*K^0.6, where Q is the output, L is the number of labor hours, and K is the amount of capital. The price of labor is $10 per hour, and the price of capital is $20 per unit. If the firm wants to produce 100 units of output, how much should it spend on labor to minimize its cost?

A. It should spend about $120 on labor. ✓
B. It should spend about $180 on labor.
C. It should spend about $240 on labor.
D. It should spend about $300 on labor.

Explanation: Cost minimization requires MPL/MPK = w/r. Here (0.4/0.6)·(K/L) = 10/20, so K/L = 0.75. Substituting K = 0.75L into Q = 10L^0.4K^0.6 = 100 gives L ≈ 11.9 and K ≈ 8.9, so labor expenditure = 10 × 11.9 ≈ $119 — about $120 (roughly 40% of the ≈ $297 total cost).

Q3. A firm’s production function is given by Q = 2L^0.4K^0.3, where Q is output, L is labor, and K is capital. If the firm wants to produce 100 units of output, and the price of labor is $10 per unit and the price of capital is $20 per unit, what is the opportunity cost of using one more unit of labor?

A. the firm must reduce its capital stock by 0.67 units ✓
B. the firm must reduce its capital stock by 0.33 units
C. the firm must reduce its capital stock by 0.4 units
D. the firm must reduce its capital stock by 0.2 units

Explanation: The opportunity cost of using one more unit of labor is determined by the ratio of the marginal products of labor and capital. The marginal product of labor (MPL) is 0.8L^(-0.6)K^0.3 and the marginal product of capital (MPK) is 0.6L^0.4K^(-0.7). The ratio of MPL/MPK = (0.8/0.6) * (K/L). To maintain the same output level, the firm must adjust capital such that the ratio of the inputs equals the ratio of their prices. The ratio of the prices is 10/20 = 0.5. Therefore, the firm must reduce its capital stock by 0.67 units for every additional unit of labor. This is because the firm is substituting labor for capital to maintain the same output level. The correct answer is derived from the ratio of marginal products, which is the opportunity cost. The ratio of MPL/MPK = (0.8/0.6) * (K/L). Setting this equal to the ratio of prices (10/20 = 0.5), we get (4/3)*(K/L) = 0.5. Therefore, K/L = 0.375. The ratio of the change in capital to the change in labor is -0.67.

Q4. In a two-good economy with fully employed resources, increasing production of good X necessarily means:

A. producing less of good Y, because resources must be shifted to X ✓
B. producing more of good Y as well
C. leaving good Y unchanged
D. increasing the output of both goods

Explanation: With all labor and capital employed, resources are scarce across uses: the production possibility frontier slopes downward, so more of one good can be obtained only by giving up some of the other (opportunity cost).

Q5. A firm is producing good X with the production function: Q_x = 2L^0.4K^0.3, where Q_x is the quantity of good X, and L and K are labor and capital, respectively. If the firm's goal is to maximize the output of good X, which of the following statements is true?

A. The firm should hire more labor and less capital to maximize the production of good X.
B. The firm should hire more capital and less labor to maximize the production of good X.
C. The firm should hire more labor and more capital to maximize the production of good X. ✓
D. The firm should hire less labor and less capital to maximize the production of good X.

Explanation: To maximize the output of good X, the firm should increase both labor (L) and capital (K) as long as the marginal product of each input is positive. The production function Q_x = 2L^0.4K^0.3 indicates that both labor and capital contribute positively to the output of good X. Therefore, the firm should hire more of both inputs to increase output.

Q6. A firm’s production function is given by Q = 2L^0.4K^0.3, where Q is output, L is labor and K is capital. If the firm is currently using 100 units of labor and 200 units of capital, what is the marginal rate of technical substitution (MRTS) of labor for capital?

A. The MRTS of labor for capital is 1.25
B. The MRTS of labor for capital is 1.6
C. The MRTS of labor for capital is 2.67 ✓
D. The MRTS of labor for capital is 3.2

Explanation: To find the MRTS of labor for capital, we need to find the ratio of the marginal product of labor (MPL) to the marginal product of capital (MPK). We can do this by taking the partial derivatives of the production function with respect to L and K. MPL = dQ/dL = 0.8L^(-0.6)K^0.3 and MPK = dQ/dK = 0.6L^0.4K^(-0.7). Then, MRTS = MPL/MPK = 0.8L^(-0.6)K^0.3 / 0.6L^0.4K^(-0.7) = (4/3)*(K/L). Then, we substitute L = 100 and K = 200 into the equation to get MRTS = (4/3)*(200/100) = 2.67

Q7. Good x uses the production function x = 2L^0.4K^0.6, while good y uses y = L^0.8K^0.2. Relative to good y, good x is:

A. more capital-intensive ✓
B. more labor-intensive
C. produced without capital
D. produced without labor

Explanation: Capital's output exponent is 0.6 for x versus 0.2 for y, while labor's is 0.4 versus 0.8, so x uses capital relatively more intensively than y does.

Q8. A firm is producing a good with decreasing marginal product of labor. If the wage rate is increased, the firm will likely shift from the production function MP+L = 120 - 2L to MP+L = 120 - 3L. What will be the effect on the labor demand curve?

A. The labor demand curve will become more inelastic. ✓
B. The labor demand curve will become more elastic.
C. The labor demand curve will shift to the left.
D. The labor demand curve will shift to the right.

Explanation: When the wage rate increases and the production function becomes steeper, the firm will be less responsive to changes in the wage rate, leading to a more inelastic labor demand curve.

Q9. A firm is producing widgets using a production function where the marginal product of labor (MPL) is decreasing as the number of workers increases. If the firm is currently employing 5 workers and the MPL is 2 widgets per worker, what will be the effect on the MPL if the firm hires 1 more worker and the total product increases by 3 widgets?

A. The MPL will remain unchanged at 2 widgets per worker.
B. The MPL will decrease to 1.4 widgets per worker. ✓
C. The MPL will increase to 2.4 widgets per worker.
D. The MPL will increase to 3 widgets per worker.

Explanation: When the MPL is decreasing, hiring more workers will decrease the MPL. Since the total product increases by 3 widgets when 1 more worker is hired, the MPL will decrease from 2 widgets per worker to 1.4 widgets per worker.

Q10. A firm is producing a good using two inputs, labor and capital. The production function is given by Q = 100L^0.4K^0.3, where Q is the quantity produced, L is the number of labor units, and K is the number of capital units. The firm's objective is to minimize costs given a fixed output level of Q = 200 units. The prices of labor and capital are $10 per unit and $20 per unit, respectively. Assuming a Cobb-Douglas production function, which of the following statements accurately describes the cost-minimizing input combination?

A. The firm will use a higher quantity of labor than capital to produce the given output level. ✓
B. The firm will use a higher quantity of capital than labor to produce the given output level.
C. The firm will use an equal quantity of labor and capital to produce the given output level.
D. The firm will use a negative quantity of labor to produce the given output level.

Explanation: Using the Cobb-Douglas production function and the given prices, we can derive the cost-minimizing input combination using the concept of isocost lines and isoquants. Since the output level is fixed, the firm will use a higher quantity of labor than capital to achieve the desired level of output while minimizing costs.

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