Q: Suppose a firm’s total cost function in the short run is $$C(q) = 100 + 5q + 2q^2$. What is the marginal cost (MC) when q = 10$?

$$MC = \frac{dC}{dq} = 5 + 4q = 5 + 4 \times 10 = 45$$

Question 1

A bakery owner is considering whether to continue using a specialized oven purchased last year for $$10,000. The oven cannot be resold or used for any other purpose. Which of the following best describes the 10$$,000 spent on the oven when making current production decisions?

Accepted Answer

It is a sunk cost and should not affect current production decisions.

Question 2

Suppose a firm’s total cost function in the short run is $$C(q) = 100 + 5q + 2q^2$. What is the marginal cost (MC) when q = 10$?

Accepted Answer

$$MC = \frac{dC}{dq} = 5 + 4q = 5 + 4 	imes 10 = 45$$

Question 3

A firm faces the following costs: fixed cost $$F = 200$$, variable cost $$VC = 10q. $$What is the average fixed cost (AFC) when $$q = 20$$?

Accepted Answer

$$AFC = \frac{F}{q} = \frac{200}{20} = 10$$

Question 4

Which of the following best explains why the marginal cost curve typically has a U-shape in the short run?

Accepted Answer

Initially, increasing marginal returns to labor lower marginal cost, but eventually diminishing marginal returns cause marginal cost to rise.

Question 5

A firm is considering two alternative uses for a machine: producing product A or product B. If the firm chooses to produce product A, it forgoes the profit it could have earned from product B. This forgone profit is best described as:

Accepted Answer

An implicit cost, which is part of the economic (opportunity) cost.

Question 6

Suppose the government imposes a specific tax of $$t$$ per unit on a firm. Which of the following best describes the effect on the firm’s cost curves?

Accepted Answer

Both the marginal cost (MC) and average cost (AC) curves shift upward by $$t.$$

Question 7

A firm’s production function is $$q = L$$^{0.5}$$K^{0.5}$$, where $$w is $$the wage rate and $$r$ is the rental rate of capital. According to the tangency rule for cost minimization, which condition must hold at the cost-minimizing input combination?

Accepted Answer

$$\frac{MPL}{w} = \frac{MPK}{r}$$

Question 8

If a firm experiences economies of scale, which of the following statements is true as output increases?

Accepted Answer

Average cost decreases as output increases.

Question 9

A firm’s long-run total cost function is $$C(q) = 50q. $$What is the long-run average cost (LAC) and marginal cost (MC)?

Accepted Answer

$$LAC = 50$$, $$MC = 50$$

Question 10

A firm produces two goods, X and Y. If the cost of producing both goods together is less than producing them separately, this is an example of:

Accepted Answer

Economies of scope

Question 11

Suppose a firm’s isocost line is given by $$C = wL + rK = 200$$, where $$w = 10$$ and $$r = 20. If $$the firm spends all its budget on labor, how many units of labor can it hire?

Accepted Answer

$$L = \frac{200}{10} = 20$$

Question 12

Which of the following is NOT a property of sunk costs?

Accepted Answer

They are relevant for current production decisions.

Question 13

A firm’s short-run average cost curve is U-shaped. If a lump-sum franchise tax is imposed, what happens to the output level at which average cost is minimized?

Accepted Answer

It remains unchanged.

Question 14

A company’s learning curve shows that average cost per unit falls as cumulative output increases. This is most likely due to:

Accepted Answer

Learning by doing, as workers and managers gain experience.

Question 15

If a firm’s production function exhibits constant returns to scale, what happens to long-run average cost as output increases?

Accepted Answer

Long-run average cost remains constant.

Question 16

A firm’s expansion path shows:

Accepted Answer

The cost-minimizing combinations of labor and capital for each output level.

Question 17

Suppose a firm’s total cost is $$C(q) = 100 + 20q. $$What is the average cost (AC) when $$q = 5$$?

Accepted Answer

$$AC = \frac{100 + 20 	imes 5}{5} = \frac{200}{5} = 40$$

Question 18

If the price of labor falls while the price of capital remains unchanged, what happens to the slope of the isocost line?

Accepted Answer

The isocost line becomes flatter.

Question 19

A firm’s cost-minimizing input combination is where the isoquant is tangent to the isocost line. At this point, which of the following must be true?

Accepted Answer

The marginal rate of technical substitution (MRTS) equals the input price ratio: $$\frac{MPL}{MPK} = \frac{w}{r}.$$

Question 20

A firm’s production function requires one unit of labor and one unit of capital to produce one unit of output. If the wage rate is $$w$$ and the rental rate of capital is $$r$$, what is the long-run cost function for producing $$q$$ units?

Accepted Answer

$$C(q) = (w + r)q$$

Microeconomics Chapter 7: Costs – Study Notes

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