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 profitmaximizing level of output? \$ to \$

Answer 1

CDW's inverse demand function is a piecewise function with P = 1,400 - 2Q for Q ≤ 200 and P = 1,100 - 0.5Q for Q ≥ 200. Changes in marginal costs have no effect on the profit-maximizing output level until they reach a point where marginal revenue equals marginal cost.

Step-by-step explanation:

The CDW's inverse demand function changes depending on whether PC Connection matches price changes or not. When PC Connection matches price cuts but not price increases, the inverse demand function for CDW's cameras would be a piecewise function. For quantities of Q ≤ 200, the inverse demand curve is P = 1,400 - 2Q, as price cuts are matched. For quantities of Q ≥ 200, the inverse demand curve is P = 1,100 - 0.5Q, as price increases are not matched.

Regarding the range of marginal cost affecting CDW's profit-maximizing level of output, we first need to determine CDW's marginal revenue. However, the question does not provide enough information to calculate marginal costs or to determine the profit-maximizing quantity. In a typical supply and demand model, any changes in marginal cost that fall below the price level where marginal revenue equals marginal cost will not affect the profit-maximizing output level. This remains true until marginal costs rise to the level where they start to affect the profit-maximizing quantity.