A chain store operates two branches. The inverse demand for one of them is P1 =

Question

A chain store operates two branches. The inverse demand for one of them is P1 = 100 2Q1 , and the inverse demand for the other is P2 = 200 3Q2 . The store’s cost of producing Q units is 10Q.

(A) Suppose that the store decides to charge different prices at the two branches. What will the equilibrium prices be?

(B) What is the resulting deadweight loss (the decrease in total surplus from the level achieved in a perfectly competitive market with one price) when the firm can set different prices at the two branches?

Explanation / Answer

9 A

Market 1

P1 = 100 2Q1 , TC1 = 10Q1

TR1 = P1*Q1 = (100 2Q1)*Q1

MR1 = dTR1/dQ1 = 100 - 4Q1

MC1 = dTC1/dQ1 = 10

For equilibrium, MR = MC

100 - 4Q1 = 10

Q1 = 90/4 = 22.5

P1 = 100 - 2*22.5 = 100 - 45 = 55

So, P1 = 55

Market 2

P2 = 200 3Q1 , T2 = 10Q2

TR2 = P2*Q2 = (200 3Q2)*Q2

MR2 = dTR2/dQ2 = 200 - 6Q2

MC2 = dTC2/dQ2 = 10

For equilibrium, MR = MC

200 - 6Q2 = 10

Q2 = 190/6 = 31.66

P2 = 200 - 3*31.66 = 105.02

So, P2 = 105.02

B

In case of perfect competition

Pc = MC = 10

So, Qc1 = (100 - 10)/2 = 45

Qc2 = (200 - 10)/3 = 63.33

So, DWL = 2[1/2(P1 - Pc)(Qc1 - Q1) + 1/2(P2 - Pc)(Qc2 - Q2)]

= 2[1/2(55 - 10)(45 - 22.5) + 1/2(105.02 - 10)(63.33 - 31.66)]

= 4021.78

If you don't understand anything then comment, I'ill revert back on the same. :)

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