Question

38. Suppose a monopolist faces two groups of consumers. Group 1 has a demand given by P1 = 50−2Q1 and MR1 = 50−4Q1. Group 2 has a demand given by P2 = 40−Q2 and MR2 = 40−2Q2. The monopolist faces MC=AVC=ATC=$10 regardless of which group she supplies to. We can infer from the demand equations that in equilibrium Group __ is the inelastic group because the elasticity at that point is __ in absolute value than that of the other group.

    (a) 1; smaller. (b) 2; smaller.

    (c) 1; larger. (d) 2; larger.

I konw the answer is a, but I don't how to solve it.

Answer 1

Consider the given problem here there are two types of consumers and their MR functions are given by, “MR1 = 50 - 4*q1” and “MR2 = 50 - 2*q2” respectively. Now, at the equilibrium “MR1 = MR2 = MC”.

=> MR1 = MC, => 50 - 4*q1 = 10, => q1 = 40/4 = 10, => P1 = 50-2*q1 = 30, => P1=30.

Now, MR2 = MC, => 40 - 2*q2 = 10, => q2 = 30/2 = 15, => P2 = 40 - q2 = 25, => P2 = 25.

So, at the equilibrium the monopolist will charge “P1=30” to group1 and “P2=25” to group2.

So, the elasticity of demand for group1 is given by, “e1 = [dq1/dP1]*(P1/q1) = [-1/2]*(30/10) = (-1.5), => |e1| = 1.5.

Now, the elasticity of demand for group2 is given by, “e2 = [dq2/dP2]*(P2/q2) = [-1]*(25/15) = (-1.67), => |e2| = 1.67. So, here we can see that at the equilibrium |e1| < |e2|, => absolute value of “e1” is less than the same of “e2”, => the demand curve for “group1” is inelastic compare to “group2”.

So, here the correct answer is “A”.