# University of Texas at Austin ECO 339 EXTRA-CREDIT PROBLEM SET,,,,,,,,,,,,,,,,,,,,,,

August 14, 2017

A country produces manufactured goods, whose industry is characterized by increasing returns toscale, monopolistic competition, and firms that differentiate their products. Firms are symmetric: allfirms have identical cost functions and demand functions given below.1Q S b P PnTC F aQwhere Q is the quantity demanded when the total industry demand is S , the number of firms in theindustry is n , the average price in the industry is P and the price charged by the firm is P . TC isthe total cost of producing Q units, where F is the fixed cost of production and a is the marginalcost of production. Assume that S does not change with the price in the industry.a) Derive an equation that relates average cost AC to n , F , S , and a . That is, derive anequation with AC on the left-hand side and n , F , S and a on the other. Hint: firmsymmetry implies that each firm charges the same price. (20 pts)b) Derive an equation that relates marginal revenue MR to P , n and b . Hint: use thedemand function to get P as a function of Q .Then, multiply it by Q to get total revenue as afunction of Q. Derive marginal revenue. Then use the demand function again, to substitutefor Q. (30 pts)c) To maximize profits, firms set marginal revenue equal to ___________________. (5 pt)d) Given your answers to b) and c) derive an equation that relates P to a , b and n . (10 pts)e) Sketch the equations from a) and d) on a graph with the number of firms n on the X-axisand the average cost and price on the Y-axis. (10 pts)f) Suppose the country opens to trade, which leads to a larger market size, S . Show the effectof this on your graph from e., labeling the new price p o and the new number of firms n o .Clearly label any curves that shift, and in which direction they shift. (20 pts)

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