Suppose you have the following information: QD = 20 - 10P + 8M (Market Demand) Q

Question

Suppose you have the following information:

QD = 20 - 10P + 8M (Market Demand)
QS = 120 + 10P - 4PI (Market Supply)

Assume M (Income) = 60, PI (Price of an input) = 5

Find P* (Market Equilibrium Price)

Assume a firm's average variable cost function has been estimated to be: AVC = 20 - 6q + q2 and that its TFC is 50

Answer the following questions for the firm that is part of this perfectly competitive industry:


7.) Determine TC at the profit-maximizing output level
8.) Determine TR when it produces q* (the profit maximizing output level)
9.) Determine its maximum profit (loss)

Explanation / Answer

(A)

QD = 20 - 10P + 8M

QD = 20 - 10P + (8 x 60) = 20 - 10P + 480

QD = 500 - 10P

QS = 120 + 10P - 4PI

QS = 120 + 10P - (4 x 5) = 120 + 10P - 20

QS = 100 + 10P

In equilibrium, QD = QS

500 - 10P = 100 + 10P

20P = 400

P = 20

Q = 100 + (10 x 20) = 100 + 200 = 300

(B) For individual firm, Total cost (TC) = TFC + TVC = TFC + (AVC x q) = 50 + 20q - 6q2 + q3

(7)

Individual firm maximizes profit when Market price = MC

MC = dTC / dq = 20 - 12q + 3q2

Equating P & MC,

20 - 12q + 3q2 = 20

- 12q + 3q2 = 0

3q2 = 12q

q = 4 (Assuming q > 0 & dividing both sides by 4q)

TC = 50 + (20 x 4) - (6 x 4 x 4) + (4 x 4 x 4) = 50 + 80 - 96 + 64 = 98

(8)

TR = P x q = 20 x 4 = 80

(9)

Profit = TR - TC = 80 - 98 = - 18 (Loss)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.