Please show calculation and explain. A monopolist sells in two geographically di

Question

Please show calculation and explain.

A monopolist sells in two geographically divided markets, East and West. Marginal cost is constant at $50 in both markets. Demand and marginal revenue in each market are as follows:

QE = 900 - 2PE

MRE = 450 - QE

QW = 700 - PW

MRW = 700 - 2QW

1) What is the profit maximizing price in each market? I believe is $375 in the West, $250 in the East

2) Calculate the total profit for this company, assuming there are no fixed costs.

3) Is there a single price this firm could charge that would generate more profits than the above?
a) Yes, but we don't know what it is

b) No, 3rd degree price discrimination is the best they can do given the information they have

c) Yes, the monopoly price

d) Yes, they could use 1st degree price discrimination

Explanation / Answer

Consider the given problem, here the demand curves of the 2 region is given,

For “East”, Pe=450 – (1/2)*Qe, => MRe = 450 – Qe.

Now, for “WEST’, Pw=700 – Qw, => MRw=700-2*Qw and MC=50.

So, at the optimum, MRe=MRw=MC=50 condition should hold.

So, by MRe=MC, => 450-Qe=50, => Qe=400, => the corresponding “Pe” is “450-(1/2)*400, =450 – 200 = 250”.

Now, by MRw=MC, => 700-2*Qw=50, => Qw=650/2=325, => the corresponding “Pw” is “700-325, =375”.

So, at the optimum, Pe=250, Qe=400 and Pw=375, Qw=325.

2).

Now, let’s assume that there are no fixed cost, => MC=AC.

So, Profit = Pe*Qe + Pw*Qw – 50*(Qw+Qe) = 250*400 + 375*325 – 50*(400+325).

=> 100,000 + 121,875 – 50*725 = 221,875 – 36,250 = 185,625 > 0.

3).

No, there don’t have any single price that can generate more profit. So, the above price and output combination will increase the profit to the maximum.

So, (b).

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