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Unformatted text preview: Econ 1 and 2 ELEMENTS OF ECONOMICS 2 LECTURE NOTES Foster, UCSD 15-Oct-09 TOPIC 7 -- MONOPOLY A. Review of Profit Maximization Rules (from Topic 5) 1. Revenue Functions: [Fig. 1] a) Let x d = d(P) be demand for the output of an individual firm . 1) If firm charges a price P, x d = d(P) is the quantity of output that this firm will be able to sell/period. 2) P = p(x d ) is the inverse demand for the individual firm's output. If the firm wishes to sell x units per period, it must charge P = p(x). 3) The law of demand holds -- the demand curve d is downward sloping. b) Important assumption. 1) The firm holds no finished product inventory and no backlog of unfilled orders. 2) Therefore, in any period, production = supply = demand: x d = x s = x p = x. c) Total revenue. 1) Total revenue received by firm = total expenditure on the firm's product by customers: TR = TE = P x. 2) Using the inverse demand function, write total revenue function TR = R(x) = p(x) x. d) Average revenue. 1) AR = TR/x = p(x)x/x = p(x) = P. 2) That is, AR = price, and the demand curve is the AR curve ! e) Marginal revenue. 1) MR is the extra revenue firm earns by selling one extra unit of output per period. 2) In tables, MR TR/ x. 3) MR and linear demand curves. [Explain] P x TR MR $ 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 $0 7 12 15 16 15 12 7 /// $7 5 3 1-1-3-5-7 $/x x x TR = R(x) MR $ Fig. 1 d = AR = p(x) Ec 1 and 2 MONOPOLY p. 2 f) Relationship of MR to price (AR). 1) MR < P for x > 1. [Fig. 2] Sell 1 unit at P = $7; TR = $7 To sell 2 units, P must fall to $6; TR = $12 2) Gain $6 on sale of second unit, but lose $1 on sale of first unit, so MR = $6 $1 = $5 < $6 = P 2. Short-Run Profit Functions: a) Total profit -- (x) = R(x) C(x) = p(x)x F V(x). b) Average profit -- (x)/x = R(x)/x C(x)/x = AR ATC = P ATC. c) Marginal profit -- /x R/x C/x = MR MC. 3. Marginal Revenue = Marginal Cost Rule: [Fig. 3] a) Profit-maximizing output x*. Problem -- find x to maximize (x) = R(x) C(x) Solution -- MR = MC at x*. b) Explanation. If x < x*, MC < MR, and an increase in x would increase . If x > x*, MC > MR, and a decrease in x would increase . c) The profit rectangle. d) For perfectly competitive firms, constant going price P* MR, and rule becomes P = MC. 4. The Short-Run Shutdown Rule: a) A firm shuts down in the SR when it lays off all variable inputs and pro-duces x = 0. TR = VC = 0 = FC b) The SR shutdown rule replaces the MR = MC rule when P < AVC. [Explain] x* C(x) R(x) (x) MC ATC d MR P* atc* Fig. 3 $/x $ * Short-Run Shutdown Rule If price is less than average variable cost, a firm maximizes profit by shutting down and producing x = 0....
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