1) A local restaurant has total costs of production given by the equation TC=48+12q+3q2 where q is thenumber of meals in a day. This implies that the firm's marginal cost is given by the equation MC = 12+ 6q (you do not need to be able to show this, just know that this is the marginal cost for the firm).
a. Write the equations showing the restaurant's average total cost and average variable cost, each as afunction of q (number of meals produced).
b. If the price of a meal in this market is $30 and the market for restaurants is characterized by perfectcompetition, how many meals will the restaurant serve to maximize profits? Calculate the firm'sprofits (or losses) at this level of output. Is this price above or below the firm's break-even price?Calculate the firm's break-even price.
c. What is the lowest price at which this restaurant would be willing to produce in the short run?Explain why this is below the break-even price found in part (b).
d. Based on your knowledge of the real world, make an argument that the restaurant industry is notperfectly competitive. Which assumptions of the perfect competition model seem to be violated?
e. Assuming the restaurant industry is perfectly competitive, how much output would be produced byeach firm in long-run equilibrium? What would be the long-run equilibrium price?
f. If the restaurant industry is perfectly competitive and consists of n identical restaurants, each withcosts functions as above, provide the equation for the industry supply curve (hint: it will include n).
g. If the market demand for meals is given by the equation QD=112-(2*P) with P being the marketprice, how many firms will be in the industry in long-run equilibrium? (Hint: You already know thelong-run equilibrium price from part e) Perfect Competition in the Long Run
2) Demand in the market for tv antennas is given by QD= 130 - 2PThe total costs for an antenna firm are TC = 25 + 5q + q2, with marginal costs thengiven by MC = 5 + 2q with q representing the quantity of antennas produced by each firm.
a. Assume that the market is open to competition and meets the conditions for a perfectly competitivemarket. What will be the equilibrium price of antennas in the long-run under conditions of perfectcompetition? How many antennas will each firm produce in the long run under perfectcompetition? How many firms will exist in the long-run competitive equilibrium?
b. What is the consumer surplus in the market for antennas in the long-run equilibrium under perfectcompetition?