Question

Consider the problem of a monopolist who is selling to two different markets (and can discriminate betwenn markets). Each market has the following isoclastic inversc demand function, where €1 < €2 < -1 1 P2 y)ky 2 1 Considcr that the firm produccs the output for both markcts in the samc factory, such that its total cost of production is given by c(y2=a 1. Calculate the price elasticity for each market. How does it change with output? 2. Solve the problem of the discriminating monopolist (find optimal quantitics and prices for cach market). n what market will the monopolist charge a higher price? 3. How do profits change if the elasticity of demand increases (i.e. becomes less elastic)?

Answer 1

Q1) We make the inverse demand function into normal demand function and then find elasticity.

We see that the elasticity is constant and is equal to the variable e₁
Similarly we do the same process for the demand function of other market and find the elasticity there to be constant and equal to e₂ .

Q2)

Solving the monopolistic problem for both the markets , this will give us the results in the image.
Interestingly enough price comes out to be equal in both the markets and is equal to b.
Quantities sold in each market will be different.

But in other cases price will be higher in the less elastic market i.e. the market where elasticity is lower.

Q3) As elasticity increases and becomes less elastic the profits will rise and monopolist can now charge a higher price as people are less willing to chang their consumptions due to change in prices.

Date Page at by, 1by KY f-K - b Peatials