PROBLEM N*4 Market demand for a homogeneous good is given by D(p) 8 -p. The incu

Question

PROBLEM N*4 Market demand for a homogeneous good is given by D(p) 8 -p. The incumbent firm's marginal cost is 4. There is a potential entrant to the market. Her marginal costs are constant and equal to o. In the absence of the entry threat what would the price in this market be? (a) ? Suppose that the game is as follows. First the incumbent firin sets the price. Then the entrant decides whether to enter the market and pay the entry cost of F. If the entry takes place, firm number 2 gets to set it's price. Because the good is homogeneous, consumers buy from the firm with the lowest price. If both prices are the same, consumers buy from the incumbent firm. b Will entry happen if c 2 and F 2? (c) Is there ? level of F for uhich entry uill be deterred uhen c= 3? Blockaded when c=3? (d Suppose that F-1. Is entry going to be deterred, accommodated, or blockaded, uhen c= 5? c = 6?

Explanation / Answer

(a) In the absence of the threat to entry, the price will be set at a point where MR is equal to MC. In this case,

TR = (8-q)*q

MR = 8-q

At equilibrium,

8-q = 4

q = 4 and p = 8-4 = 4

(b) Entry will only happen if the entrant can set a price lower than the incumbent and extract all the market from the incumbent.

Now if c = 2 and F = 2,

TC = 2 + 2q

Profit = TR - TC = (8- q)q - 2- 2q

Maximizing with respect to q

8 - q - 2 = 0

q = 6, p = 2

Since it is less than 4, entrant will earn a revenue of 12 and total cost of 2 + 2(6) = 14 and the profits will be negative, hencr despite a lesser price than the incumbent, the entrant would not enter.

(c) MR = MC

8 - q = 3

q = 5, p = 3.

TR = 15 , TC = F + 3(5) = F + 15

For F = 0, entry will be deterred and for any F > 0, the entry will be blockaded

(d) c= 5

8 - q = 5

q = 3, P = 5

TR = 15 , TC = 1+ 5(3) = 16

Entry will b blocked

c = 6

8- q = 6

q = 2, p = 6

TR = 12, TC = 1 + 6(2) = 17

Entry will be blocked

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