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PS8 - optimal price(p the cartel should choose d Use the...

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UCLA Economics 11 Fall 2006 Professor Mazzocco Problem Set 8 Due by November 25 before 7:00pm in the box located outside room 2221E. 1) OPEC can price gasoline as it wishes. Suppose that it knows how demand responds to changes in prices (p). In particular, it knows that the quantity of barrels of gasoline demanded (Q) is given by the following function: Q=a*e (-1/5)p , where “a” is just a constant. a) Write an expression for OPEC ’s revenues as a function of Q . b) Given that the OPEC only faces a fixed cost, the total cost function is given by: C(q)=50. Now write an expression for the cartel’s pro fit function (as a function of Q). c) Solve the profit maximization problem to find the optimal quantity (Q*) and the
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Unformatted text preview: optimal price (p*) the cartel should choose. d) Use the second order condition to show that the cartel is actually maximizing profits when it chooses this optimal quantity and price. 2) Suppose that the cost function of a firm is given by: C(q) = 100 + 5q 2 a) Find Fixed and Variable cost. b) Find marginal cost. c) Find the average cost and the average variable cost. d) Draw the relationship between MC and AC. Suppose that the firm is a price-taker and that the current market price is 100. e) Is it optimal for the firm to shut down or to continue production?...
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