A multi-product monopolist produces two products that are substitutes

Marketing Dec 22, 2020

A multi-product monopolist produces two products that are substitutes. The demand for a product depends on both the price of the goods and the price of the other product. Demand functions are:

q1=100−2p1+p2q2=100−2p2+p1q1=100−2p1+p2q2=100−2p2+p1

The marginal cost of producing each good is constant with c1=c2=20c1=c2=20.

a) What is the own-price elasticity of demand for good 1?

b) What is the cross-price elasticity of demand?

Expert Solution

a) Price elasticity of demand

q1 = 100-2P1+P2

2P1 =100-q1+P2

P1 =50-0.5q1+0.5P2

Ped=P1q1×dq1dP1Ped=P1q1×dq1dP1

Ped=P1q1×(−2)Ped=P1q1×(−2)

Ped=50−0.5q1+0.5p2q1×(−2)Ped=50−0.5q1+0.5p2q1×(−2)

b) Cross price elasticity of demand

Ced=P2q1×dq1dP2Ced=P2q1×dq1dP2

Ced=P2q1×(1)Ced=P2q1×(1)

Ced=q1−100+2P1q1×(1)

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