Topic 5: Cost Curves and Cost Minimization
Topic 5 Practice Questions
1. Nick owns an ice cream parlour. He spends $650 on two inputs, capital and labour. He pays $14 an hour to his labourers and the rental cost of capital is $24 per hour. Assuming capital is plotted on the vertical axis and labour is plotted on the horizontal axis, determine the slope of the isocost line.
(A) 12/7
(B) -7/12
(C) 7/12
(D) 12/5
Correct Answer: B
Steps:
The slope of the isocost line
= ΔK/ΔL= −(w/r)
= -14/24
= -7/12
2. Bob runs a small firm. The total cost function is:
TC = 1000 + 10q + 10q2
If Bob wanted to minimize the average total cost, which of the following output levels would he choose?
(A) 1/10
(B) 11
(C) 20
(D) 10
Correct Answer: D
Steps:
The average total cost reaches its minimum when ATC = MC.
Step 1: Find MC
MC = ΔTC / Δq = 10 + 20q
Step 2: Find ATC
ATC = TC / q = (1000 + 10q + 10q2 ) / q = 1000 / q + 10 + 10q
Step 3: Set MC = ATC
1000 / q + 10 + 10q = 10 + 20q
Multiply both sides of the equation by q:
1000 + 10q + 10q2 = 10q + 20q2
1000 = 10q2
100 = q2
q =10
The average total cost is minimized at q = 10.
3. Assume the price of labour is $12 and the price of capital is $25. For a total cost of $150, what is the isocost equation?
(A) 150 = 12L * 25K
(B) 150 = 25L + 12K
(C) 150 = 12L + 25K
(D) 25 = 150L – 12
(E) None of the above
Correct Answer: C
4. Consider two firms: Firm A and Firm B. Each produces a single product. Assume these two firms merge, which increases the cost associated with producing both goods. ___________ are present in production.
(A) Economies of scale
(B) Diseconomies of scale
(C) Economies of scope
(D) Diseconomies of scope
Correct Answer: D
5. Mr. Brown is a famous investor on Wall Street. He becomes tired of trading stocks and wants new challenges. He quits his job and starts his own business. Mr. Brown used to earn $200,000 a year as an investor. Now, he pays himself $105,000 a year. In addition, he pays $10,000 a year for the factory building he rents and $20,000 a year for the equipment that he rents to run his business. What is the economic cost of the time that Mr. Brown contributes to his start-up business?
(A) $220,000 a year
(B) $95,000 a year
(C) $200,000 a year
(D) $230,000 a year
Correct Answer: B
Explanation:
The economic cost of the time that Mr. Brown contributes to his start-up business is: $200,000 – $105,000 = $95,000 a year.
6. Suppose Firm A is paying its workers $15/hr and rents capital at a rate of $10/hr. Assume the cost of labour increases by $5/hr. What would happen to the isocost line? Calculate the slope of the new isocost line and predict what will happen to the input combination used in production.
(A) The isocost line will shift to the left; the new slope will equal -0.5; both labour input and capital input will decrease.
(B) The isocost line will shift to the right; the new slope will equal -1.5; both labour input and capital input will increase.
(C) The isocost line will rotate inward; the new slope will equal -2; labour input will decrease and capital input will increase.
(D) The isocost line will rotate outward; the new slope will equal -0.5; labour input will increase and capital input will decrease.
Correct Answer: C
Steps:
The slope of the new isocost line = -20/10 = -2. The horizontal intercept decreases and the isocost line rotates inward. Because the cost of labour increases, Firm A will use fewer units of labour and more units of capital.
7. As total output increases, which of the following statements regarding short-run cost functions is correct?
(A) Average variable cost increases.
(B) Total cost and variable cost increase by the same amount.
(C) Average fixed cost remains unchanged.
(D) Average fixed cost decreases.
(E) Both B and D.
Correct Answer: E
Steps:
As output increases in the short-run, the total variable cost increases. Nevertheless, the average variable cost could increase or decrease. The fixed cost is independent of the output level. Average fixed cost decreases as the output level increases.
8. You are the manager of a Nike factory and you oversee the production of Nike Tech tracksuits. You employ 50 workers and the wage rate is $20 an hour. Moreover, you use 10 machines at an hourly rental rate of $400. Assume the production function is: q = 2L + 10K. Currently, you are producing 200 units of suits an hour. The CEO has decided to reward managers and the only criterion is whether or not the factory minimizes its production costs. Do you think that you will receive an award? If the answer is no, before the end of the fiscal year, how would you change the input combination?
Answer:
In this production process, labour and capital are perfect substitutes.
MPL / W = 2/20 = 0.1
MPK / r = 10/400 = 0.025
MPL / W > MPK /r
Therefore, to minimize the total cost, you would have to use a corner solution. You should only use labour in production.
Currently, your total cost = 20 * 50 + 400 * 10 = 5000
Given $5000, the optimal labour input = 5000 / 20 = 250
The output level = 2L+10K = 2 * 250 + 10 * 0 = 500.
9. True or false:
If a firm achieves economies of scale, it automatically achieves economies of scope.
Answer: False
Explanation:
No direct relationship exists between economies of scale and economies of scope. Economies of scale refer to the production of one good, whereas economies of scope refer to the production of two or more goods.
10. Suppose the long-run total cost function is C(q) = 4q2. What is the cost-output elasticity?
(A) 2
(B) 4
(C) ¼
(D) 1
(E) ½
Correct Answer: A
Steps:
The cost-output elasticity Ec = MC/AC
Given C(q) = 4q2
MC = ΔC/Δq = 8q
AC = C/q = 4q
Therefore, Ec = 8q/4q = 2
11. Are the following statements regarding short-run cost functions true or false:
(i) When marginal product decreases, the marginal cost rises.
(ii) Fixed cost increases with the level of output.
(iii) If the marginal cost is greater than the average total cost, the average total cost must be decreasing.
Answer:
(i) True
(ii) False
(iii) False
Explanation:
Both (ii) and (iii) are false. Fixed cost does not vary with the level of output. When the marginal cost is greater than the average total cost, the average total cost is increasing.
12. Which of the following statements is false?
(A) Accounting cost is also known as the sunk cost.
(B) Economic cost includes both explicit cost and implicit cost.
(C) Accounting cost only considers the actual monetary cost.
(D) A firm’s expenses for office supplies and utilities are included in the accounting costs.
Correct Answer: A
13. A restaurant owner rents kitchen equipment for $32 an hour and pays his employees $20 an hour. If the owner’s MPK = 4 and MPL = 2.5, which of the following is true?
(A) The owner can reduce the cost of production at his current output by increasing labour inputs and lowering capital inputs.
(B) The owner can reduce the cost of production at his current output by increasing capital inputs and lowering labour inputs.
(C) The owner is currently minimizing cost at his current output.
(D) The owner can reduce the cost of production at his current output by lowering both labour and capital inputs.
(E) The owner can reduce the cost of production at his current output by increasing both labour and capital units.
Correct Answer: C
Steps:
MPL/w = 2.5/20 = 0.125
MPK/r = 4/32 = 0.125
MPL/w = MPK/r. Therefore, the current input combination is optimal, and the owner is minimizing the total cost of production.
14. A pizza parlour has recently expanded to accommodate more customers due to its growing popularity. The kitchen and restaurant space doubles. In addition, the parlour doubles its orders of pizza ingredients to keep up with the rising demand. Before the expansion, the parlour incurred a total cost of $800 a week for 1,000 pizzas. After expansion, the cost became $1,500 a week for 2,000 pizzas. This is an example of:
(A) diseconomies of scale.
(B) diseconomies of scope.
(C) increasing returns to scale.
(D) economies of scope.
(E) economies of scale.
Correct Answer: E
Steps:
Economies of scale occur when a doubling of output requires less than a doubling of cost. Another way to think of this concept is that the average cost decreases as the output level increases. In this case, initially, AC = $800 / 1,000 = 0.8. After expansion, AC = $1,500 / 2,000 = 0.75. AC decreases with the output level, which indicates that the pizza parlour achieves economies of scale.
15. Consider isoquants that slope downward and are convex. Are the following statements true or false:
I. As we move downward along an isoquant, it becomes more and more difficult to substitute one input for another while keeping the output unchanged.
II. Assume increasing returns to scale. The isoquants will move further apart from each other as inputs are increased proportionately.
(A) Both I and II are true.
(B) I is true and II is false.
(C) I is false and II is true.
(D) Both I and II are false.
Correct Answer: B
Steps:
With increasing returns to scale, the isoquants become closer and closer together as the inputs increase proportionately.
16. Jennifer started a small business in 2010. Today, the business is worth $450,000. Assume that the market interest rate is 5%. Corporation A would like to buy Jennifer’s business next year for $462,500, and Corporation B would like to buy the business today for $450,000. If Jennifer keeps the business for another year, she can make a profit of $10,000. What should she do?
(A) Get more information to answer the question.
(B) Sell to Corporation A.
(C) Sell to Corporation B.
(D) Jennifer is indifferent to selling to either corporation.
Correct Answer: D
Steps:
If Jennifer sells to Corporation B this year, the present value = $450,000.
If she operates for one more year and then sells to Corporation A next year, the present value = ($462,500 + $10,000) / 1.05 = $450,000.
Both options would generate the same present value. So, Jennifer is indifferent between the two options.
17. A firm’s total cost function is: TC = 2000 + 2Q + 5Q2. Which of the following statements is false?
(A) ATC = 2000/Q + 2 + 5Q
(B) AFC = 2000/Q
(C) TVC = 5Q2
(D) MC = 2 + 10Q
Correct Answer: C
Steps:
TVC = TC – TFC
= 2000 + 2Q + 5Q2 – 2000
= 2Q + 5Q2
18. A car wash company hires workers and rents equipment to provide its services. The company wants to wash 240 cars an hour. Currently, it pays its workers $12 an hour and has a rental cost of $3 an hour. The production function is given as: Q = 15KL. Find the optimal input combination that minimizes the firm’s total cost.
Answer: The optimal bundle of inputs is L = 2, K = 8.
Steps:
Q = 240 units
r = $3
w = $12
Q = 15KL
MPK = ΔQ/ΔK = 15L
MPL = ΔQ/ΔL = 15K
At the optimal input combination,
MRTSL,K = w/r
15K/15L = 12/3
K = 4L
Q = 240 units
15KL = 240
Sub K = 4L into 15KL = 240
15*(4L)*L = 240
L2 = 4
L = 2
K = 4L = 8
Thus, the optimal bundle of inputs is L = 2, K = 8
19. Which of the following statements is false:
(A) When marginal cost equals average cost, the average cost is minimized.
(B) When marginal cost > average cost, the average cost is increasing.
(C) When marginal cost > average cost, the average cost is decreasing.
(D) When marginal cost < average cost, the average cost is decreasing.
Correct Answer: C
20. A firm has $1,000 to spend on two inputs: labour, graphed on the horizontal axis, and capital, graphed on the vertical axis. If the hourly wage for workers is $30 and the hourly cost of capital is $60, what is the slope of the isocost curve?
(A) –1/2
(B) -2
(C) 30/60
(D) 2
Correct Answer: A
Steps:
The isocost equation is: 30L + 60K = 1,000
Rewrite this equation:
The slope = –1/2
21. Steven is a stock trader. At the beginning of last year, he invested $10,000 in stocks after saving, which he could have put into the bank and earned interest at a rate of 5% per year. Moreover, it turned out that the stocks he invested in performed poorly last year, and he only received 70% of his principal back at the end of the year. What is the opportunity cost for Steven, having invested the money instead of earning interest in a bank?
(A) $3,000
(B) $500
(C) $3,500
(D) $4,000
Correct Answer: C
Steps:
Steven has two options:
- Option 1: Invest money in the stock market. The value of Option 1 at year-end = 10,000 * 70% = $7,000
- Option 2: Put money into a bank and earn an annual interest of 5%. The value of Option 2 at year-end = 10,000 * (1+5%) = $10,500
The opportunity cost = $10,500-$7000 = -$3,500
22. Consider the validity of the following statements:
I. Economic cost may be lower than accounting cost.
II. Sunk cost should not influence decision making.
A) I is true and II is false.
B) I is false and II is true.
C) Both I and II are true.
D) Both I and II are false.
Correct Answer: B
Explanation:
Statement I is false. Accounting cost only includes explicit costs, while economic cost includes both explicit and implicit costs. Thus, economic cost is never lower than accounting cost.
23. Suppose Andy’s firm uses both capital input (K) and labour input (L) in production. The production function is given as:
Q = K0.75L0.25
The cost of labour is $3 a unit, and the cost of capital is $5 a unit. The cost-minimizing capital-labour ratio (K/L) is ____.
(A) 9/5
(B) 3/1
(C) 5/9
(D) 1/3
Correct Answer: A
Steps:
MPL = 0.25 * K0.75L-0.75
MPK = 0.75 * K-0.25L0.25
MRTSL,K = MPL/ MPK = (0.25 * K0.75L-0.75) / (0.75 * K-0.25L0.25) = K/3L
Set MRTSL,K = w / r
K/3L = 3/5
K/L = 9/5
The cost-minimizing capital-labour ratio K/L = 9/5.
Topic 5 H5P Interactive Questions
