Question 1

Suppose a firm's total cost function is given by $$C(q) = 10 + 4q^2$. What is the marginal cost (MC) function?

Accepted Answer

$$MC(q) = 8q$$

Question 2

Given the cost function $$C(q) = 10 + 4q^2$, what is the average total cost (ATC) when q = 2$?

Accepted Answer

$$ATC = 11$$

Question 3

If the fixed cost (FC) is $$10$$ and the variable cost (VC) is $$4q^2$$, what is the average fixed cost (AFC) when $$q = 5$$?

Accepted Answer

$$AFC = 2$$

Question 4

A firm has a production function $$F(L, K) = K L$$ with $$K = 4$$ fixed in the short run. If the wage $$w = 2$$ and the rental rate $$r = 3$$, what is the total cost function $$C(q)$$?

Accepted Answer

$$C(q) = 12 + \frac{q}{2}$$

Question 5

In the long run, which of the following statements is TRUE regarding costs?

Accepted Answer

Long run costs are weakly lower than short run costs because all inputs are variable.

Question 6

Given the isocost line $$C = wL + rK$$, if $$w = 10$$, $$r = 20$$, and $$C = 1000$$, which of the following combinations of $$(L, K) is on $$the isocost line?

Accepted Answer

$$(L = 50, K = 25)$$

Question 7

If a firm’s production function is $$F(L, K) = K$$^{0.5}$$L^{0.5}$$ with $$K = 4 in $$the short run, $$w = 2$$, and $$r = 3$, what is the total cost function?

Accepted Answer

$$C(q) = 12 + \frac{q^2$}{2}$$

Question 8

Which of the following best describes the slope of an isocost line?

Accepted Answer

$$-\frac{w}{r}$$

Question 9

A firm wants to produce 300 units of output. If the cost-minimizing input bundle is $$L = 150$$ and $$K = 75$$, with $$w = 10$$ and $$r = 20$$, what is the total cost?

Accepted Answer

$$C = 3000$$

Question 10

Which condition must be satisfied at the cost-minimizing input bundle in the long run when isoquants are smooth?

Accepted Answer

$$MRTS = \frac{w}{r}$$

Question 11

If the average variable cost (AVC) is $$4q$$ and the average fixed cost (AFC) is $$\frac{10}{q}$$, what is the average total cost (ATC)?

Accepted Answer

$$ATC = 4q + \frac{10}{q}$$

Question 12

Which of the following best describes the expansion path in the context of cost minimization?

Accepted Answer

It is the curve that traces all cost-minimizing input bundles as output changes.

Question 13

If a firm’s marginal cost (MC) is increasing, which of the following is most likely true about the production function?

Accepted Answer

The marginal product of the variable input is decreasing.

Question 14

In the short run, which cost component does NOT change as output increases?

Accepted Answer

Fixed cost (FC)

Question 15

Suppose the wage rate $$w$$ increases while the rental rate $$r$$ remains constant. What happens to the slope of the isocost line?

Accepted Answer

The isocost line becomes steeper (in absolute value increases).

Question 16

If $$C(q) = 12 + \frac{q^2$}{2}$$, what is the marginal cost (MC) when $$q = 4$$?

Accepted Answer

$$MC = 4$$

Question 17

Which of the following is a correct interpretation of the marginal rate of technical substitution (MRTS)?

Accepted Answer

The rate at which labor can be substituted for capital while keeping output constant.

Question 18

If a firm’s cost function is $$C(q) = 12 + \frac{q}{2}$$, what is the average variable cost (AVC) when $$q = 4$$?

Accepted Answer

$$AVC = 0.5$$

Question 19

Which of the following is NOT a property of the long run in production theory?

Accepted Answer

All inputs are fixed.

Cost of Production: Short Run and Long Run Analysis

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