Explain step by step 1. [3 points Suppose that a competitive firm\'s marginal co

Question

Explain step by step

1. [3 points Suppose that a competitive firm's marginal cost of producing output q is given by MC(q) 3+2q. Assume that the market price of the firm's product is S9 a. What level of output will the firm produce? Show your work. b. What is the firm's producer surplus? Show your work. c. Suppose that the average variable cost ofthe firm is given by AVC(g) 3+g. Suppose that the firm's fixed costs are known to be $3. What is the firm's profit in the short run? Show your work. IHint: Profit is total revenue minus total cost. You do have enough information to calculate both total revenue and total cost here.]

Explanation / Answer

(a) A competitive firm maximizes profit by equating Price with MC.

3 + 2q = 9

2q = 9 - 3 = 6

q = 6/2 = 3

(b) Producer surplus(PS) is the area between supply curve (MC) and price.

Competitive supply function equals its MC. So, Supply function is:

P = MC

P = 3 + 2q

When q = 0, P = 3 (Minimum acceptable price, the vertical intercept of supply curve).

So, PS = (1/2) x $(9 - 3) x 3 = (1/2) x $6 x 3 = $9

(c) Total cost (TC) = Fixed cost (FC) + Total variable cost (TVC), where

TVC = AVC x q & q = 3, P = 9

TC = 3 + [q x (3 + q)] = 3 + (3q + q2) = 3 + [(3 x 3) + (3 x 3)] = 3 + (9 + 9) = 21

Total revenue, TR = P x q = 9 x 3 = 27

Profit = TR - TC = $(27 - 21) = $6

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