Microeconomics, marginal cost profit maximization, final exam practice problems
(The attached PDF file has better formatting.)
*Question 1.1: Marginal Revenue
Assume the demand curve is linear.
At P = $100, total revenue is $200,000.
At P = $80, total revenue is $240,000.
What is the marginal revenue per unit at P = $120?
80
100
120
140
160
Answer 1.1: B
The demand curve is Q = α – β × P
At P = $100, total revenue = $200,000, so Q = 2,000
At P = $80, total revenue = $240,000, so Q = 3,000
We use these values to solve for α and β in the demand curve.
2,000 = α – β × 100
3,000 = α – β × 80
A
1,000 = 20 β A β = 50 and α = 7,000Q = 7,000 – 50P, so at P = 120, Q = 1,000.
We used a demand curve as Q in terms of P, so we convert to P in terms of Q before finding the marginal revenue curve.
P = 7,000 / 50 – 0.02Q = 140 – 0.02Q
The total revenue curve is TR = 140Q – 0.02Q2.
The marginal revenue curve is MR = 140 – 0.04Q.
At P = $120, Q = 1,000, and marginal revenue is 140 – 0.04 × 1,000 = $100
*Question 1.2: Profit Maximization
A firm faces a demand curve of P = 130 – 5Q. The marginal cost for this firm is 20 + Q, and fixed costs are 50. The firm produces a quantity and charges a price to maximize profits. What is the marginal revenue curve facing the firm?
MR = 130Q – 5Q2
MR = 130 – 5P2
MR = 130Q – 10Q2
MR = 130 – 10Q
MR = 130P – 5P2
Answer 1.2: D
Total revenue = 130Q – 5Q2
Marginal revenue = M(Total revenue)/MQ = 130 – 10Q
*Question 1.3: Profit Maximization
A firm faces a demand curve of P = 130 – 5Q. The marginal cost for this firm is 20 + Q, and fixed costs are 50. The firm produces a quantity and charges a price to maximize profits. What is the quantity produced by the firm? (Assume a continuous distribution.)
2
6
10
14
18
Answer 1.3: C
Set marginal revenue = marginal cost:
130 – 10Q = 20 + Q A 110 = 11Q
110 = 11Q A Q = 10 A P = 80
*Question 1.4: Profit Maximization
A firm faces a demand curve of P = 130 – 5Q. The marginal cost for this firm is 20 + Q, and fixed costs are 50. The firm produces a quantity and charges a price to maximize profits. What is the price charged by the firm? (Assume a continuous distribution.)
50
60
70
80
90
Answer 1.4: D
Set marginal revenue = marginal cost:
130 – 10Q = 20 + Q A 110 = 11Q
110 = 11Q A Q = 10 A P = 80
*Question 1.5: Profit Maximization
A firm faces a demand curve of P = 130 – 5Q. The marginal cost for this firm is 20 + Q, and fixed costs are 50. The firm produces a quantity and charges a price to maximize profits. What are the variable costs of the firm? (Assume a continuous distribution.)
200
250
300
350
400
Answer 1.5: B
variable costs = I 20 + Q dQ from 0 to 10 = 20Q + ½ Q2 from 0 to 10 A
variable costs = 20 × 10 + ½ × 100 = 250
*Question 1.6: Profit Maximization
A firm faces a demand curve of P = 130 – 5Q. The marginal cost for this firm is 20 + Q, and fixed costs are 50. The firm produces a quantity and charges a price to maximize profits. What are the total costs of the firm? (Assume a continuous distribution.)
200
250
300
350
400
Answer 1.6: C
variable costs = I 20 + Q dQ from 0 to 10 = 20Q + ½ Q2 from 0 to 10 A
variable costs = 20 × 10 + ½ × 100 = 250
total costs = 250 + 50 = 300
*Question 1.7: Profit Maximization
A firm faces a demand curve of P = 130 – 5Q. The marginal cost for this firm is 20 + Q, and fixed costs are 50. The firm produces a quantity and charges a price to maximize profits. What is the total revenue of the firm? (Assume a continuous distribution.)
400
500
600
700
800
Answer 1.7: E
130 – 10Q = 20 + Q A 110 = 11Q
110 = 11Q A Q = 10 A P = 80
Total revenue = 10 × 80 = 800
*Question 1.8: Profit Maximization
A firm faces a demand curve of P = 130 – 5Q. The marginal cost for this firm is 20 + Q, and fixed costs are 50. The firm produces a quantity and charges a price to maximize profits. What is the net profit of the firm? (Assume a continuous distribution.)
400
500
600
700
800
Answer 1.8: B
130 – 10Q = 20 + Q A 110 = 11Q
110 = 11Q A Q = 10 A P = 80
Total revenue = 10 × 80 = 800
variable costs = I 20 + Q dQ from 0 to 10 = 20Q + ½ Q2 from 0 to 10 A
variable costs = 20 × 10 + ½ × 100 = 250
total costs = 250 + 50 = 300
Net profit = 800 – 300 = 500