Question

Problem 2: In problem 1, the monopolist sells a product with a total cost function: TC = 1,000 + 500Q + Q?. The market demand curve is given by the equation: Q = 500 -0.25P But now assume that the government imposes a $100 per unit tax on Q. (a) Who What price and quantity would be expected if the firm is allowed to operate unregulated except for the imposed tax? Show the tax result on your graph of Problem 1. Denote P, Q, and MC.

Answer 1

Cilver) - Domand - 500 -0.25 p 0.245 P = 500 - 8 pe 9.2001259 PE 2000 - 4Q [TR = 2,000Q - 4927 MR = d e = 2000- 897 Demand f? Total revenue for {P.Q} ...do • "lotal Cast function TC = 1000 + 500 g +02 Mc = det - 500+2037 Sol The equilibrium price and quantity determine by the first order cond (foc) of profit maximisation. Zet 20} fact T = TR-TC - profit f? T= 20000 - 40" - 1000 - 500g - Q2 15000 - 502 - 1000 foc da, 1500 - 100 =0 a = 150/ equilibrum quantity soe ve = -10 <0 second order conda y satisfied I equilibrium price p= 2000 - 4(150) [P Pt (Чо ° /

6 # Gout impose per unit tax = $100 B is per imit tey than the amount of tao.cill be - TT=8Q here ß = $100 TE 1007 Here cost will be 3 Tc = TC +T = 1000+500 R + Q2 +1009 TC' = 1000+ 600 g +0?? [ Me' = arc = 600420] now equilibrium price. & quantity determine by the FOG of porofit maxinusatom. Maliit | A' = TP - T H a' - 20000 -402 - 1000 - 600Q -02 t = 1400Q - 50² - 1000 E 1400-10QFO de a = 1407 equilibrium equantity soc 10.40 satisfied #equilibrium price pe 2000 - 4(140) = 2000 - 560 p =$ 1440

Price 2000 -na (600+22) ma p=14401 ---- P=14001 (500+26) Goo! 500 ... 'AR. (2000-40) (2006-8a) L uantity gQ =150 = 140