Q: Given the production function $$q = 10L - 0.5L^2$, what is the marginal product of labor (MPL) when L = 4$?

$$MPL = 10 - 0.5 \times 2 \times 4 = 6$$

Q: If a firm’s short-run cost function is $$TC = 2q^2$ + 10q + 100$$, what is the average total cost (ATC) when $$q = 5$$?

$$ATC = \frac{2 \times 25 + 10 \times 5 + 100}{5} = 24$$

Question 1

Suppose a firm's production function is $$q = 5L$$^{0.5}$$K^{0.5}$$, where $$L is $$labor and $$K$ is capital. If the firm uses 16 units of labor and 9 units of capital, what is the total output produced?

Accepted Answer

30

Question 2

Given the production function $$q = 10L - 0.5L^2$, what is the marginal product of labor (MPL) when L = 4$?

Accepted Answer

$$MPL = 10 - 0.5 	imes 2 	imes 4 = 6$$

Question 3

A firm faces the following short-run cost function: $$SVC = q^2$ + 40q$$, and fixed cost $$FC = 400. $$What is the average variable cost (AVC) when $$q = 10$$?

Accepted Answer

$$AVC = \frac{100 + 400}{10} = 50$$

Question 4

If a firm’s total cost is $$TC = 2000$$ and its total revenue is $$TR = 2500$$, what is the accounting profit?

Accepted Answer

$$500$$

Question 5

Suppose a firm’s production function is $$q = 2L + 3K. If $$the firm uses 5 units of labor and 4 units of capital, what is the marginal product of capital (MPK)?

Accepted Answer

$$MPK = 3$$

Question 6

A firm’s short-run marginal cost (MC) is given by $$MC = 2q. If $$the firm produces 8 units of output, what is the marginal cost of producing the 8th unit?

Accepted Answer

$$MC = 16$$

Question 7

Given the following table for a firm’s output and total product of labor, what is the average product of labor (APL) when 4 workers are employed and total output is 32?

Accepted Answer

$$APL = \frac{32}{4} = 8$$

Question 8

If a firm’s short-run average total cost (ATC) is $$ATC = \frac{TC}{q}$$ and total cost $$TC = 500$$ when output $$q = 25$$, what is the ATC?

Accepted Answer

$$ATC = 20$$

Question 9

A firm’s profit-maximizing output occurs where marginal cost equals marginal revenue. If $$MC = 10$$ and $$MR = 8$$, what should the firm do to maximize profit?

Accepted Answer

Decrease output

Question 10

Suppose a firm’s short-run cost function is $$TC = q^2$ + 20q + 100. $$What is the marginal cost (MC) function?

Accepted Answer

$$MC = 2q + 20$$

Question 11

If a firm’s production function is $$q = 4L$$^{0.5}$$K^{0.5}$, and the firm doubles both labor and capital, what happens to output?

Accepted Answer

Output quadruples

Question 12

A firm’s short-run average fixed cost (AFC) is $$AFC = \frac{FC}{q}. If $$fixed cost $$FC = 200$$ and output $$q = 10$$, what is the AFC?

Accepted Answer

$$AFC = 20$$

Question 13

If a firm’s short-run variable cost (SVC) is $$SVC = 3q^2$, what is the marginal cost (MC) when q = 5$?

Accepted Answer

$$MC = 30$$

Question 14

Suppose a firm’s total revenue is $$TR = 1000$$, total cost is $$TC = 1200$$, and implicit costs are $$300. $$What is the economic profit?

Accepted Answer

$$-500$$

Question 15

A firm’s production function is $$q = 10L - 0.5L^2$. At what value of L$ does the marginal product of labor (MPL) become zero?

Accepted Answer

$$L = 20$$

Question 16

If a firm’s short-run cost function is $$TC = 2q^2$ + 10q + 100$$, what is the average total cost (ATC) when $$q = 5$$?

Accepted Answer

$$ATC = \frac{2 	imes 25 + 10 	imes 5 + 100}{5} = 24$$

Question 17

A firm’s short-run profit is maximized when $$MR = MC. If$$ $$MR = 15$$ and $$MC = 20$$, what should the firm do?

Accepted Answer

Decrease output

Question 18

Suppose a firm’s production function is $$q = 6L$$^{0.5}$$K^{0.5}$, and the firm uses 9 units of labor and 16 units of capital. What is the output?

Accepted Answer

36

Question 19

If a firm’s short-run cost function is $$TC = q^2$ + 10q + 100$$, what is the marginal cost (MC) when $$q = 4$$?

Accepted Answer

$$MC = 2 	imes 4 + 10 = 18$$

Question 20

A firm’s production function is $$q = 8L$$^{0.5}$$K^{0.5}$. If the firm uses 25 units of labor and 16 units of capital, what is the output?

Accepted Answer

64

Short Run Firms: Production, Cost, and Profit Analysis

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