Question 1

Suppose a firm has the production function $$F(L, K) = 10K$$^{0.5}$$L^{0.5}$$ and capital is fixed at $$K=1$. What is the expression for the average product of labor (APL)?

Accepted Answer

$$APL = 10L$$^{-0.5}$$

Question 2

Given the same production function $$F(L, K) = 10K$$^{0.5}$$L^{0.5}$$ with $$K=1$, what is the marginal product of labor (MPL)?

Accepted Answer

$$MPL = 5L$$^{-0.5}$$

Question 3

A firm with production function $$F(L, K) = 3L$$^{1/3}$$K^{2/3}$$, fixed $$K=1$$, wage $$w=3$$, and rental rate $$r=5$$ wants to produce $$q$$ units. What is the total cost function $$C(q)$?

Accepted Answer

$$C(q) = 5 + \frac{q^3$}{9}$$

Question 4

Refer to the isoquant-isocost diagram (first image). If the wage rate is $$16$$ and the rental rate of capital is $$20$$, what is the cost-minimizing combination of labor and capital to produce $$q=20$$ units?

Accepted Answer

Labor = 4, Capital = 5, Total Cost = $$164$$

Question 5

A competitive firm’s total cost function is $$C(q) = 100 + 4q^2$. If the market price is 10$, what is the profit-maximizing output level?

Accepted Answer

$$q^* = 1.25$$

Question 6

For the same firm as above, what is the profit at the profit-maximizing output when $$p=10$$?

Accepted Answer

$$-93.75$$

Question 7

A competitive market has cost function $$C(q) = 10q$$ for each firm and market demand $$Q(p) = 200 - 5p. $$What is the equilibrium price?

Accepted Answer

$$p^* = 10$$

Question 8

Given the same market, what is the equilibrium quantity?

Accepted Answer

$$Q^* = 150$$

Question 9

A monopoly faces $$Q(p) = 50 - \frac{p}{2}$$, with constant marginal cost $$MC = 16$$ and no fixed costs. What is the profit-maximizing quantity?

Accepted Answer

$$q^* = 21$$

Question 10

For the monopoly above, what is the profit-maximizing price?

Accepted Answer

$$p^* = 58$$

Question 11

For the monopoly above, what is the profit at the profit-maximizing output?

Accepted Answer

$$882$$

Question 12

Refer to the cost curves diagram (second image). What does the highlighted curve represent?

Accepted Answer

the portion of the short-run supply curve where the firm produces positive output

Question 13

If a competitive firm produces nothing when price is $$5$$ but produces $$100$$ units when price is $$10$$, what can you infer about the firm's average variable cost (AVC)?

Accepted Answer

The minimum value of AVC lies between $$5$$ and $$10$$

Question 14

Which of the following best describes the effect of first-degree price discrimination by a monopolist compared to single-price monopoly?

Accepted Answer

Consumer surplus is zero, producer surplus is maximized, and deadweight loss is eliminated.

Question 15

If the slope of an isocost line is $$-0.8$$, what does this imply about the relative prices of labor and capital?

Accepted Answer

The wage rate is $$0.8$$ times the rental rate of capital.

Question 16

If a firm's marginal cost curve lies above its average variable cost curve for all output levels, what does this imply about the firm's shut down condition?

Accepted Answer

The firm will never shut down in the short run.

Question 17

Returns to scale refer to:

Accepted Answer

How output changes as all inputs are increased proportionally.

Microeconomic Theory: Cost Minimization, Short-Run Supply, and Isoquants

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