Question

Crusty Cakes sells donuts in Eastown and Westown. Its total costs are given by TC = 10(Q_E + Q_W). The demand in each neighborhood is given by Q_E = 100 – 2P_E and Q_W = 100 – P_W . If Crusty price discriminates between the two neighborhoods, how much are its maximized profits?

Question 5 options:

A)

$850.

B)

$1,200.

C)

$2,475.

D)

$2,825.

E)

$3,250.

Answer 1

In case of price discrimination, monopolist will maximize profit in each market.

We know that

Q=QE+QW

So,

TC=10*(QE+QW)=10Q

Marginal Cost=dTC/dQ=10

Now take the case of Eastown,

QE=100-2PE

2PE=100-QE

PE=50-0.5QE

Total Revenue=TRE=PE*QE=(50-0.5QE)*QE=50QE-0.5QE^2

Marginal Revenue=MRE=dTRE/dQE=50-QE

Set MRE=MC

50-QE=10

QE=40

PE=50-0.5QE=50-0.5*40=$30

Total Revenue=TRE=PE*QE=30*40=$1200

Now take the case of Westown,

QW=100-PW

PW=100-QW

Total Revenue=TRW=PW*QW=(100-QW)*QW=100QW-QW^2

Marginal Revenue=MRW=dTRW/dQW=100-2QW

Set MRW=MC

100-2QW=10

2QW=90

QW=45

PW=100-45=$55

Total Revenue=TRW=PW*QW=55*45=$2475

Monopolist's total revenue=TR=TRW+TRE=2475+1200=$3675

Total Cost=TC=10*(QW+QE)=10*(45+40)=$850

Monopolist's total Profit=TR-TC=3675-850=$2825

Correct option is

D) $2825