PC Connection and CDW are two online retailers that compete in an Internet marke

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 = 1,400 - 4Q. When it does not match price changes, CDW’s inverse demand curve is P = 1,120 -0.5Q. Based on this information, determine CDW’s inverse demand function over the last couple of months.

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

Explanation / Answer

The question describes a market pertaining to kinked demand model by Paul Sweezy. Here we are given that when PC Connection matches CDW’s price changes, the inverse demand curve for CDW’s cameras is given by P = 1,400 - 4Q. When it does not match price changes, CDW’s inverse demand curve is P = 1,120 -0.5Q.

Hence we find the intersection point of sticky price and quantity over which the market has an equilibrium

1400 - 4Q = 1120 - 0.5Q

280 = 3.5Q

Q* = 80 units and P = 1080

Now this implies, if Q is > 80, we have an inelastic demand curve P = 1400 - 4Q and for Q < or = 80, we have an elastic demand curve P = 1120 - 0.5Q

Now marginal revenues are MR1 = 1120 - Q and MR2 = 1400 - 8Q. For Q > 80, we have MR = 1120 - 80 = 1040.and for Q < 80, MR = 1400 - 8*80  = 760 . When Q = 80, MR is discontinuous over the range (1040, 760) and this is the range for MC.

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