Question

4. In the competit ve market for widgets there are 50 identical consumers and 200 iden tical firms. Each individual consumer has the following demand function for widgets P(P) 100 2P where qD is the quantity an individual consumes and P is the widget's price. Each firm has the following cost function: C() 100 2qq (a) (3 points) Find the market demand function for widgets QP(P). Find the industry supply function for widgets Qs(P), make sure to find each firm's supply function before you find the supply function for the industry as a whole. (b) (4 points) What is the equilibrium price in this industry? How many widgets does each consumer consume? How many widgets does each firm produce? How much of a profit or loss does each firm make? What is 4 (c) (4 points) Suppose the firm's long-run cost function is C(g) 25+ the long run competitive equilibrium price P and quantity Q (hint: find the minimum long-run average cost)? How many firms are in the market? (d) (6 points) Suppose the government provides exclusive rights single firm and Q2 to a making other producers illegal. The firm's cost function is C(Q) = 20, 000 +2Q+ Set up the monopolist's problem and solve for Q and P. What is the Monopo- list's profit? What is the Dead Weight Loss here? How many widgets does each consumer consume now? - 100

Answer 1

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P 2 26-2 =12 each fim pndues So 2 uidgcts eeuel = 2612) / 12) 2 2C122 - 24 14y 312- 26 25 LR eq uili bri um and miu. AC CC2) AC= 22 25 AC 25 4 dAC -R5 d z 22 dAC put 2 9 irm wiu po duaco LR ea ch So CS Scanned with CamScanner uni ts widjes \0 NN

Ac C 25 10 5 m c vacte AC cauilibrsun pica P =s Thus 5 st0 5 600 5 o So Number ot frrms, n 45 o intue meutcet 50 fims So Noo 5000 5o 50- MR 50 2/& - 2 CLA) 26, 060 + 2a CS Scanned with CamScanner

dc M C 2 20 fmonopy MR = ( Prolit nuay. Cond) 2 Q 2 2a 5o-2 2g 25 50- 50- 1260 P = 50-12 = 38 Monopalist's 2u20 381260 (l20)2 - 20000- 2460 5660 1200x126 45600 22400 ahh 4560 368 60 07 feTfeut ormperi tiru ond = M C 50- 2 2.8 CS Scanned with CamScanner

5 o-2 28 3Q 4860 7 So So-160ro 5o-16 3u 5 0 Pm 38 Pe 92 DD MR 2 2.00 66D 2 So (38- 2) 6o-120o) DWL 1 CS Scanned with CamScanner 2460