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International Trade and Investments - ECO339K University of Texas at Austin Jacek Rothert Fall 2012 EXTRA-CREDIT PROBLEM SET (Maximum Points: 100)...

I mainly need help with parts a, b, d, e, and f.

International Trade and Investments - ECO339K University of Texas at Austin Jacek Rothert Fall 2012 EXTRA-CREDIT PROBLEM SET (Maximum Points: 100) Due: Friday, December 7 th , in class First name: 1 pt. Last name: 2 pts. Homework in one piece: 2 pts. A country produces manufactured goods, whose industry is characterized by increasing returns to scale, monopolistic competition, and firms that differentiate their products. Firms are symmetric: all firms have identical cost functions and demand functions given below.   1 Q S b P P n TC F aQ     where Q is the quantity demanded when the total industry demand is S , the number of firms in the industry is n , the average price in the industry is P and the price charged by the firm is P . TC is the total cost of producing Q units, where F is the fixed cost of production and a is the marginal cost 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 an equation with AC on the left-hand side and n , F , S and a on the other. Hint: firm symmetry 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 the demand function to get P as a function of Q .Then, multiply it by Q to get total revenue as a function of Q. Derive marginal revenue. Then use the demand function again, to substitute for 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-axis and 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 effect of this on your graph from e., labeling the new price o p and the new number of firms o n . Clearly label any curves that shift, and in which direction they shift. (20 pts)
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We have Q= S[(1/n)- b(P-Ṗ)] and TC= F+aQ.
a) We are given that all firms in the industry are symmetric. Therefore each firm charges
the same price.
i.e. Ṗ=P, the average price in the industry...

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