Respuesta :
Answer:
a) The firm will produce 4.50 units of output
b) Producer surplus is $20.25
c) In short run run, the profit would be positive.
Explanation:
Suppose that a competitive firm's marginal cost of producing output q (MC) is given by MC(q) = 6 + 2q. Assume that the market price (P) of the firm's product is $15.
a) What level of output (q) will the firm produce?
b) What is the firm's producer surplus?
c) Suppose that the average variable cost of the firm (AVC) is given by AVC (q ) = 6 + 1q. Suppose that the firm's fixed costs (FC) are known to be $20. Will the firm be earning a positive, negative, or zero profit in the short run.
a) What level of output (q) will the firm produce?
Given that MC(q) = 6 + 2q; to maximize profit, the marginal cost should be equal to the market price.
∴ 6 + 2q = $15
2q = 15 - 6
2q = 9
q = 9/2
q = 4.50 units
The firm will produce 4.50 units of output
b) What is the firm's producer surplus?
Producer surplus is the area below the market price of $15 and above the marginal cost curve of 6 + 2q which is linear. This gives a triangle with base of 4.50 (since q = 4.50) and height of $15 - $6 = $9
Producer surplus = area of triangle = 1/2 × base × height = 1/2 × 4.5 × 9 = 20.25
Producer surplus is $20.25
c) Suppose that the average variable cost of the firm (AVC) is given by AVC (q ) = 6 + 1q. Suppose that the firm's fixed costs (FC) are known to be $20. Will the firm be earning a positive, negative, or zero profit in the short run.
Profit = total revenue - total cost
total cost = total variable cost + total fixed cost
Total variable cost = q × AVC(q) = 4.5 × (6 + 4.5) = 4.5 × 10.5 = $47.25
total cost = total variable cost + total fixed cost = $47.25 + $20 = $67.25
Total revenue = Price × quantity = $15 × 4.5 = $67.5
Profit = total revenue - total cost = $67.5 - $67.25 = $0.25
In short run run, the profit would be positive.
Question:
Marginal cost of producing output q (MC) is given by MC(q) = 6 + 2q. Assume that the market price (P) of the firm's product is $15. What level of output (q) will the firm produce?
What is the firm's producer surplus?
Suppose that the average variable cost of the firm (AVC) is given by AVC(q) = 6 + q. Suppose that the firm's fixed costs (FC) are known to be $20. Will the firm be earning a positive, negative, or zero profit in the short run?
Answer:
1. $4.5
2. $20.25
3. $0.5
Explanation:
A. Given
MC(q) = 6 + 2q.
Market price (P) = $15.
The evel of output (q) will the firm produce is calculated as follows;
Marginal cost of producing = Market price = $15
By Substitution;.
$15 = $6 + 2q
Make q the subject of formula
2q = $15 - $6
2q = $9
q = $9/2
q = $4.5
b. Given that
MC(q) = 6 + 2q. --;;; 1
Where MC(q) = $15
Because, MC(q is linear and the producer surplus forms a triangle bounded by base of 2q and height of q
Make 2q the subject of formula in (1)
2q = 15 - 6
2q = 9
And q = 4.5
Area = ½ b * h
Area = ½ * 4.5 * 9
Area = 20.25
Hence, the producer surplus is $20.25
3.
Profit = Total Revenue - Total Cost
The total revenue is calculated by price * quantity
Total Revenue = $15 * 4.5 = $67.5
Total cost = Total Variable Cost + Fixed cost
The total variable cost is equal to AVC(q) when q = $4.5 and AVC = 6 + q
So, AVC(q) = (6+q)(q)
= (6 + 4.5)(4.5)
= 47.25
Fixed cost= 20
Total Cost = 47.25 + 20 = 67.25
So, Profit = $67.5 - $67.25
Profit = $0.25
Therefore, the firm is earning positive economic profits.
