# What will be the price quantity demanded and profits for each firm at the equilibrium?

T Show more Question 1 (25 points) The total and marginal cost functions for a typical soft coal producer are: TC = 75000 + 0.1q2 and MC = 0.2q where q is measured in railroad cars per year. The industry consists of 55 identical producers. The market demand curve is: QD = 140000 425P where P is the price per carload and QD is total market demand. The market can be regarded as competitive. a. Calculate the short run equilibrium price and quantity in the market. b. Calculate the quantity that each firm would produce. c. Calculate the firms profit (or loss). d. Calculate producer surplus consumer surplus and total surplus at the equilibrium (Hint: if you draw a figure of market demand and market supply curves it will be easier for you to solve for the surplus.) ? ? ? ? ? ? Question 2 (20 points) Suppose that the total cost function of a firm is given as TC = 1000 + 10Q 2 a. Determine the output level that minimizes average total cost (ATC). At this output level find TC ATC MC. b. Determine the output level that minimizes average variable cost (AVC). At this output level find TC ATC MC. ? ? ? ? Question 3 (20 points) Suppose Race Car Motors (RCM) has two divisions the upstream one that manufactures engines and supplies to the downstream division which assembles the automobiles and sells them. The upstream divisions only customer is the downstream one and each car requires exactly one engine. RCM has the following demand for its automobiles. P = 20000 Q The downstream divisions total cost of assembling and selling cars is CA(Q) ? 8000Q The upstream divisions total cost of producing engines is Where Q is the number of cars produced and QE is the number of engines produced. a. Write down the profit equations of downstream division upstream division and total profits. b. How many engines and cars should the firm produce in order to maximize profits? What should be the optimal transfer price for engines? c. Calculate the profit earned by the upstream division the downstream division and the firm as a whole. ? ? ? Question 4 (25 points) Two firms compete by choosing price. Their demand functions are Q1 ? 20 ? P1 ? P2 and Q2 ? 20 ? P1 ? P2 where P1 and P2 are the prices charged by each firm respectively and Q1 and Q2 are the resulting demands. Marginal costs are zero and no fixed cost. a. Suppose the two firms set their prices at the same time. What will be the price quantity demanded and profits for each firm at the Nash-Bertrand equilibrium? b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What will be the price quantity demanded and profits for each firm at the equilibrium? (Hint: it is the Stackelberg Model for price competition. You can solve this problem in the same way as what we have discussed about the Stackelberg Model for output competition but here the choice variable is PRICE). c. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set prices at the same time; (ii) You set your price first; or (iii) Your competitor sets price first. If you could choose among these options which would you prefer? Explain why. ? ? ? ? ? ? ? ? ? ? ? Question 5 (10 points) The following matrix shows the payoffs for an advertising game between Coke and Pepsi. The firms can choose to advertise or not to advertise. Numbers in the matrix represent profits; the first number in each cell is the payoff to Coke; the second number in each cell is the payoff for Pepsi (Numbers in millions). ? ? ? Coke (rows)/Pepsi (columns) Advertise Dont Advertise Advertise (10 10) (500 -50) Dont Advertise (-50 500) (100 100) a. Does either firm have a dominant strategy? b. Explain why this would be described as a Prisoners Dilemma game. What is the Nash equilibrium? Show less