Question

Q3) Assume that the manufacturing of cellular phones is a perfectly competitive industry. The market demand...

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: QD=(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 + q2 + 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 QS= 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.

Homework Answers

Answer #1

TC = 100 + q2 + 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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