Question

4. The demand for product X is PX = 10 − 2X – Y, where Y is the quantity of a substitute product that currently is not being produced. The marginal cost of X is a constatn equal to $1. Entry is completely barred and a monopolist, “Incubment” produces X.

1. Find Incumbent’s price, quantity, and profit.

2. Incumbent wishes to investigate the possibility of introducing Y, which is also protected from entry by other firms. The demand for Y is PY = 10 − 2Y – X and it also has a constant marginal cost of $1. However, there is a fixed cost of introducing Y of $4. Find the values of X, Y, PX , PY and profit for Incumbent when it introduces Y. Will Incumbent introduces Y?

c. Now assume that entry is no longer barred. For simplicity, assume that if a new firm, “Entrant,” decides to introduce Y, then Entrant and Incumbent will collude perfectly and settle at the joint profit maximum. This implies that the prices and quantites ofund in part b will apply. Will Entrant have an incentive to introduce Y?

d. Still assuming that entry is not barred, will Incumbent have an incentive to preempt the entry by Entrant and offer Y first? (It is assumed that if Incumbent offers Y, then a second seller of Y will have negative profits.)

Answer 1

4)a) given Y is not being produced ,so Y=0

Px=10-2x

MR=10-4x

MC=1

10-4x=1

X=9/4=2.25

Px=10-2*2.25=10-4.5=5.5

Profit=(5.5-1)*2.25=4.5*2.25=10.125

B)Px=10-2x-y

MRx=10-4x-y

MC=1

10-4x-y=1

X=(9-y)/4=2.25-0.25y,. Equation 1

Py=10-2y-x

MRy=10-4y-x

10-4y-x=1

Y=(9-x)/4=2.25-0.25x. , Equation 2

Putting equation 2 into 1,.

X=2.25-0.25(2.25-0.25x)

X=2.25-0.5625+0.0625

X=1.6875/0.9375=1.8

Y=2.25-0.25*1.8=1.8

Px=10-2*1.8-1.8=10-5.4=4.6

Py=10-2*1.8-1.8=4.6

Profit=(4.6-1)*(1.8+1.8)-4=3.6*3.6-4=12.96-4=8.96

Because profit is lower ,so incumbent won't introduce Y .

C)As given the result will be ,

X=1.8

Y=1.8

Px=4.6

Py=4.6

So profit of entrant=(4.6-1)*1.8 -4=3.6*1.8-4=2.48

Positive profit will give incentive to entrant to introduce Y.

D) profit of incumbent when entrant introduce Y.

Px=4.6

X=1.8

Profit=(4.6-1)*1.8=3.6*1.8=6.48

Profit of incumbent when it introduce Y too by himself.

Profit=8.96

So higher profit give incentive to incumbent to introduce Y before entrant .