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.

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

This is the case of kinked demand curve in oligopoly market which assumes that firms are trying to maintain their market share and the rival firms might match the price fall but are unable to match the price increase.

Now, we need to find the quantity at which the kink occurs with respect to the two demand curves.

Let, P=1000-2Q----(i)

        P=700-0.5Q----(ii)

Comparing equation (i) and (ii), we get:

1000-2Q=700-0.5Q

Or, -1.5Q=-300

Or, Q=300/1.5= 200 cameras

Putting Q=200 in equation (i), we get:

                P=1000-2*200= $600

Again, putting Q=200 in equation (ii), we get:

P=700-0.5*200 = $600

Hence, both the demand curve shares the point P= $600 and Q=200

Now, in order to determine which inverse demand applies in which case, we will need to find the price elasticity of both the curves:

We know, price elasticity of demand is calculated by percentage change in quantity demanded by percentage change in price, I.e.,

Ed= ∆Q/∆P*P/Q

Here, P=$600 and Q= 200

For equation (i):

P=1000-2Q

Or, Q=500-0.5P

∆Q/∆P= -0.5

Therefore, e_d = -0.5*(600/200) =-1.5

For equation (ii),

P=700-0.5Q

Or, Q=1400-2P

∆Q/∆P= -2

Therefore, e_d = -2*(600/200) =-6

Here, elasticity is lower for equation (i) and higher for equation (ii)

Thus, P=700-0.5Q<=200

          P=1000-2Q>=200

Now, in order to find the specified range, we have to calculate marginal revenue at Q=200, where marginal revenue refers to additional revenue gained by producing an additional unit of output.

Marginal Revenue = ∂TR/∂Q

Total revenue (TR) =p*q

For equation (i)

TR = (1000-2Q)*Q= 1000-2Q²

Marginal Revenue = ∂TR/∂Q =1000-4Q

For, Q=200

MR=1000-4*200 = $200

Again for equation (ii),

TR = (700-0.5Q)*Q = 700-0.5Q²

MR = ∂TR/∂Q

        =700-Q

For, Q=200

MR = 700-200 =$500

Therefore, the required range is $200 to $500