Question

1. Consider a monopolist selling in two markets. The demands in markets 1 and 2 are given by

   q1 =100−p1
   q2 =120−1/2p2

   Marginal cost is constant and given by MC = 20. There are no fixed costs. Find a) optimal output, price in market 1, b) optimal output and price in market 2 and c) total profit. What can we say about demand elasticities of the two markets at the optimal outputs?

Answer 1

ca) 9, = 100 - Pi P = 100-9 TRI = P,Q, - (100-2, ) 2 TR, = 100q, qe MR, = J TRI 09. = 100 (1) -29, MR, 2100-29, MC=20 Condition profit-maximizing MR, = mc 100-29, = 20 22; = 100-20 9, 40 units, substituting & into P = 100 - no - Go Pi equation

(b) 12 - १२0 - 0.52 0.sh - १२० - १, 2 - १२० -१ १ - २५० - 2 TRI = 22 - (२५० --29, 22 - २०१, - २१ HR, OTP = २५० (1) -५ profit - maximizing Condition _ MR, = ( २५० -५१ = २० ५१. २५० -२० 9 - २२० 22 = ss units.

substitating Is into price ke equation P = ano –2 (55) =240-110 = 130 Totul potit = TR, IT R₂ - TC (c) = Piz, + R2 - MC (2 +22) = 6o xuot 130xSS - 20 (notss) =anoo + 7150 - 20(95) = 9sso -190 = 7650 akt I Elasticity of demand in 9, =loo-pl olz, di = 0-1 =-1 Ed = da, & Pi 1 2

Edi = -1 & 60 = -1.5 Elastic demand) Elasticity of demand in mkt ? 22 = 1or 1 l 4P 30 - 400 = -130 -1.18 Ed > Hence Elastic demand