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.
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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