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 - 2Q. When it does not match price changes, CDW’s inverse demand curve is P = 1,100 -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

Given that when price is matched (inelastic demand portion), the inverse demand curve is P = 1,400 - 2Q and when price is not matched (elastic demand portion), demand is P = 1,100 -0.5Q.

Based on this information, the demand function is composed of two segments one elastic and other inelastic.

P = 1,100 - 0.5Q if Q ≤ 200

P = 1,400 - 2Q if Q ≥ 200

Corresponding marginal revenue functions are

MR = 1100 - Q and MR = 1400 - 4Q

Now the quantity in this market is found at the kink which is

1100 - 0.5Q = 1400 - 2Q

1.5Q = 300

Q = 300/1.5 = 200 units

At 200 units, the marginal revenue ranges from 1400 - 4*200 = $600 to 1100 - 200 = $900

Over the range of $600 to $900 changes in marginal cost there will be no effect on CDW’s profit-maximizing level of output which remains fixed at 200 units.