Question

A monopolist has a cost function given by c(y) = y and faces an inverse demand curve given by P(y) = 156.00 - y, where P is the per-unit price and y is the quantity of output sold. Assume this monopolist cannot discriminate and charges a single price. What is the profit-maximizing level of output? What is its profit-maximizing price? $ Part 2 (2 points) See Hint Assume you want to choose a price ceiling for this monopolist so as to maximize total surplus (consumer surplus + producer surplus). What price ceiling level should you choose? $ What quantity would be produced at this price ceiling?

Answer 1

What is the profit-maximizing level of output? 39 What is its profit-maximizing price? $ 117

What price ceiling level should you choose? $ 104 What quantity would be produced at this price ceiling? 52

Suppose that you put a tax on the monopolist of $20 per unit of output. What is its profit-maximizing level of output now? 44

- » dtc cy) = y² This is the Total Cast (TC) function TC= 42 ey Cy4) но 2ч 1 Наласыл со расхіна | dy iteou PCy) - 156 – ч Tл , а Дилазе лише била | - AR = 156 - • Dunand function - ARXY = (156-y)xy. - TR = 15by-y2 - Total revenue function - d TR = d (15 by- y²) MR MR = 156-2y) = 156-2y | Marginal runnue function] Marginal runnue function TC = 42 - AC - y - Aurage Cast function

Profit Maximining wil of output is when MR=MC MR = MC - 156-2y = 24 »/311) Profit Maximining price The demand at y=39 D = 156-39 mould priung The monopoleest MR = APC 156-24 =4 - he subject to average cost I Demand at y=52 = 156-52 =104 e price A quantity With the a $20 per mupply cunce tax unit will to dicuare hy $20 Remember New MC the firns MC curve is its - 24 - 20 supply curue New MC = MR - 24 -20 = 156-2y. y = 144 I

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