Question

PC Connection and CDW are two online retailers that compete in an Internet market for digital cameras. While the products they sell are similar, the firms attempt to differentiate themselves through their service policies. Over the last couple of months, PC Connection has matched CDW’s price cuts, but has not matched its price increases. Suppose that when PC Connection matches CDW’s price changes, the inverse demand curve for CDW’s cameras is given by P = 1,200 - 2Q. When it does not match price changes, CDW’s inverse demand curve is P = 900 -0.5Q. Based on this information, determine CDW’s inverse demand function over the last couple of months.

P = ____- ____ Q if Q ≤ 200

      ____- ____ Q if Q ≥ 200

Over what range will changes in marginal cost have no effect on CDW’s profit-maximizing level of output?

$ _____to $ _______

Answer 1

PC Connection and CDW are the two firms which compete in the market for digital cameras. The market structure is similar to that of a oligopolistic market. The kinked demand theory states that the firms are dependent on each others pricing strategies, where each firm responds to the price cuts of its competitors but ignores the price rise.

Thus, in this case the demand curve is gave as,

P = 900 - 0.5Q , if Q ≤ 200

P = 1200 - 2Q, if Q ≥ 200.

Now, in order to find the price range we substitute Q = 200 at each Marginal Revenue(MR) curves.

When Q ≤ 200,

P = 900 - 0.5Q

P*Q = 900Q - 0.5Q^2 = Total Revenue (TR)

d TR / d Q = MR = 900 - Q

Substituting Q = 200 in the above MR function,

MR = 900 - 200 = 700

Again, when Q ≥ 200 ,

P = 1200 - 2Q

P*Q = 1200Q - 2Q^2

d TR/dQ = 1200 - 4Q = MR

Substituting Q = 200 in the above MR function again,

MR = 1200 - 4*200 = 400

Thus, at Q = 200, MR1 = 700 and MR2 = 400,

So, the price range is $400 to $700.