Question

Q3) Assume that the manufacturing of cellular phones is a
perfectly competitive industry. The market demand for cellular
phones is described by a linear demand function:
Q^{D}=(6000-50P)/9. There are 50 manufacturers of cellular
phones. Each manufacturer has the same production costs. These are
described by long-run total cost functions of TC(*q*) = 100
+ q^{2} + 10q.

1) Show that a firm in this industry maximizes profit by producing q = (P-10)/2

2)Derive the industry supply curve and show that it is
Q^{S}= 25P – 250

3)Find the market price and aggregate quantity traded in equilibrium

4)How much output does each firm produce? Show that each firm earns zero profit in the equilibrium.

Answer #1

TC = 100 + q^{2} + 10q

(1) Firm's supply function is its Marginal cost (MC), where

MC = dTC/dq = 2q + 10

Firm supply function: P = 2q + 10

2q = P - 10

q = (P - 10) / 2

(2) Industry supply (QS) = 50q, therefore

q = QS/50

P = 2 x (QS/50) + 10

P = (QS/25) + 10

25P = QS + 250

QS = 25P - 250

(3) Equating QD & QS,

(6,000 - 50P) / 9 = 25P - 250

6,000 - 50P = 225P - 2,250

275P = 8,250

P = 30

Q = [6,000 - (50 x 30)] / 9 = (6,000 - 1,500) / 9 = 4,500 / 9 = 500

(4) Firm output (q) = Q / 50 = 500 / 50 = 10

At this P & q combination,

Average cost (AC) = TC / q = (100 / q) + q + 10 = (100 / 10) + 10 + 10 = 10 + 10 + 10 = 30

Since Price = AC, profit is zero.

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