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 = 1,000 - 2Q. When it does not match price changes, CDW’s inverse demand curve is P = 700 -0.5Q. Based on this information, determine CDW’s inverse demand function over the last couple of months.

I got the first part, P=700-.5Q if Q is less than or equal to 200, and 1000-2Q if Q is greater than or equal to 200. I can't figure out how to find the range in which changes in marginal cost have no effect on CDW's profit-maximizing level of output.

Answer 1

When PC Connection matches CDW’s price changes, the inverse demand curve is P = 1,000 - 2Q. This is inelastic demand that lies below the kink in kinked demand curve condition. Its marginal revenue is MR1 = 1000 - 4Q.

When it does not match price changes, CDW’s inverse demand curve is P = 700 -0.5Q. This is elastic demand curve and that lies above the kink. Its marginal revenue is MR2 = 700 - Q.

Note that the quantity at the kink is where two demand functions meet

1000 - 2Q = 700 - 0.5Q

300 = 1.5Q

Q = 200.

Hence kink occurs at Q = 200 so demand function P = 1,000 - 2Q is operative for Q > or = 200 and demand function P = 700 -0.5Q is operative for Q < or = 200

Also note that in a kinked demand the respective marginal revenue functions are discontinuous at the kinked quantity, Find MR1 and MR2 at the kinked quantity Q = 200 which will give you the range within which Marginal cost can varry

MR1 = 1000 - 4*200 = 200

MR2 = 700 - 200 = 500

Hence the range in which changes in marginal cost have no effect on CDW's profit-maximizing level of output is from $200 to $500.