1 [25 points] An perfectly competitive industry consists of N firms, each one of which has a cost function given by: , where qi is the output of firm i in any given period. The per period market demand for this industry is given by P = 20 – 4Q. [5 points] What is the industry supply function?
QUESTION
1 [25 points] An perfectly competitive industry consists of N firms, each one of which has a cost function given by: , where qi is the output of firm i in any given period. The per period market demand for this industry is given by P = 20 – 4Q.
 [5 points] What is the industry supply function?
 [5 points] What is the equilibrium market price and quantity?
 [5 points] What is the per period profit of each firm?
 [6 points] Suppose a N+1 firm can enter this industry but must pay an entry cost of 1. The firm will compare the present discounted value of its profits after entry with the entry cost. It will enter if the present discounted value of the profits exceeds the entry cost and stay out otherwise. If the firm’s discount factor is δ = 0.9 and the firm expects no change in the demand and supply sides of this industry would it want to enter the industry if N=10? How about if N=20?
Assume that the entrant takes into consideration the effect that its entry will have on the market price. Also note:
 [4 points] What is the maximum number of the firms that will enter the market?
2 [45 points] Suppose there is a market which the incumbent firm is already in. The market demand is given by P = 32 – Q. The incumbent (I) firm’s cost function is given by C_{I} (q_{I}) = 8q_{I}. There is a potential entrant (E). The entrant has a cost function is C_{E} (q_{E}) = 8q_{E} + 16.
 [6 points] Suppose the entrant stays out of the market. What would be the optimal quantity that the incumbent wants to produce? What would be the profit? Show your work.
 [8 points] Suppose the entrant has already entered the market. The incumbent and the entrant now play a Cournot duopoly. How many units would each firm produces? Find the price and each firm’s profit under the equilibrium quantities. Sow your work.
 [5 points] Assuming the entrant is in the market, the incumbent wants to fight. Specifically, the incumbent wants to produce q_{I} = 20. Given this, find the entrant’s optimal quantity to produce. Find the price and each firm’s profit under the quantities. Show your work.
 [6 points] Relying on the above results, draw the game tree and the payoffs of the following game. The entrant first decides whether to enter or not. If the entrant enters, the incumbent decides whether to compete as in (ii) and or producing q_{I} = 20. If the entrant does not enter, the incumbent maximizes a monopoly profit.
 [5 points] Find the subgame perfect equilibrium of the above game. Show your work.
 [3 points] Going back to the beginning of the question, suppose the entrant did not yet enter. The incumbent already produced q_{I} = 20. Assuming the entrant does not enter; find the price and incumbent firm’s profit. Show your work.
 [7 points] Given the above results, draw the game tree and the payoffs of the following game. The incumbent chooses first. She may not fix the quantity. The other choice is to produce q_{I} = 20. In any case, the entrant decides whether to enter or not. If the incumbent chose not to fix the quantity, the incumbent maximizes a monopoly profit or plays a Cournot duopoly depending on the entrant’s decision. If the incumbent chose to produce q_{I} = 20, the incumbent cannot change the quantity regardless of the entrant’s choice.
 [5 points] Find the equilibrium of the above game.
3 [30 points] The only manufacturer of transporters in the planet of Telasia is Telemetafores, which is using an outdated plant with a production cost of 10 per transporter. Telemetafores can upgrade the plant at a cost of 100. The upgrade will result in a production cost of 7 per transporter. The optimal price and corresponding sales are given by the table below:
Unit Cost  Optimal Price  Quantity Sold  
Upgrade  7  14  120 
Not Upgrade  10  18  100 
 [6 points] Calculate profits in each case. Should Telemetafores choose to upgrade?
Another company, StoTsaka, is considering of entering the Telasia market for transporters by building a stateoftheart plant at a cost of E. This plant produces transporters at a cost of 7 per transporter. The cost of Telemetafores are given above (and depend on whether Telemetafores upgrades the plant or not). The optimal price and corresponding sales for the two firms if StoTsaka enters the market are given below as a function of whether Telemetafores does or does not invest in the upgrade of its plant.
Optimal price  Optimal Quantity  
Telemetafores  StoTsaka  Telemetafores  StoTsaka  
Upgrade  12  12  80  80 
Not Upgrade  15  13  50  90 
 [8 points] What are the profits of Telemetafores and StoTsaka as a function of whether Telemetafores invests or does not invest in the upgrade of its plant, assuming that StoTsaka decides to enter the market? [
 [4 points] Use the information in parts (a) and (b) above to fil out the matrix of payoff for the normal form of the game between Telemetafores and StoTsaka, assuming that the two firms make their respective decisions (the former whether to upgrade the plant or not to upgrade, the latter whether to enter the market or not to enter) simultaneously. Use the fact that if StoTsaka does not enter the market, its profit is zero.
Telemetafores  StoTsaka  
Enter  Not enter  
Upgrade


Not upgrade

 [6 points] How low does E have to be for “Not Enter” to be a dominated strategy for StoTsaka? That is, for what values of E is the strategy “Not Enter” dominated by the strategy “Enter”?
 [6 points] If the entry cost E is equal to 300, fill out the matrix of payoffs again. What is the Nash Equilibrium of the game?
Telemetafores  StoTsaka  
Enter  Not enter  
Upgrade


Not upgrade

ANSWER
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