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ECONOMICS

THEORY OF UNCERTAINITY.

PLEASE DO IT MATHEMATICALLY.

Consider the problem of deciding optimal production levels under uncertainty, where the producer is an EU maximizer with Bernoulli index u(x). Suppose that the total cost of producing q units is c(q)=21q2, and u(x)=A+x, where A>0 is very large. a. Suppose initially that the price is known to be P>0 per unit. Find the optimal output level, q, and resulting profit. b. Suppose now that the price the individual face, P, is a random variable and can be 0 or 2P with probability 0.5. Write the first-order condition that characterizes the optimal output level, q. Do you expect q to be smaller than q ? Why, or why not? c. Suppose that someone offers her a future contract that locks her price at P. Write an equation that characterizes the maximum value that she would be willing to pay for this future Consider the problem of deciding optimal production levels under uncertainty, where the producer is an EU maximizer with Bernoulli index u(x). Suppose that the total cost of producing q units is c(q)=21q2, and u(x)=A+x, where A>0 is very large. a. Suppose initially that the price is known to be P>0 per unit. Find the optimal output level, q, and resulting profit. b. Suppose now that the price the individual face, P, is a random variable and can be 0 or 2P with probability 0.5. Write the first-order condition that characterizes the optimal output level, q. Do you expect q to be smaller than q ? Why, or why not? c. Suppose that someone offers her a future contract that locks her price at P. Write an equation that characterizes the maximum value that she would be willing to pay for this future