1. The firm's profit function is defined by T(q, x; 3) = s(q-x) + fx-c(q). (1)...

 

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1. The firm's profit function is defined by T(q, x; 3) = s(q-x) + fx-c(q). (1) The firm produces q units of output at cost c(q) such that c(0) 0, c'(q) > 0 and c"(q) > 0. The firm sells x units in the futures market at price f and sells the remaining q- x units in the spot market at random price š. Assume that s takes on two values, p+ ε₁ and p + E2 such that ₁ > 0> 2> -p. In other words, the random spot price š is defined by the gamble (2) <p+E1, p + E2; α > = where a € (0, 1). (a) Write down the profit gamble conditional on q and x. (b) Set up the maximization problem of an agent with utility function u(7) such that u' (T) > 0 and u" (π) <0. (c) Provide a graphical solution of the maximization problem. That is, sketch precisely the set of available gambles and illustrate the solution that maximizes the expected utility of profits. In particular, what is the opportunity cost of ₁ in terms of ₂ (via hedging)? 1. The firm's profit function is defined by T(q, x; 3) = s(q-x) + fx-c(q). (1) The firm produces q units of output at cost c(q) such that c(0) 0, c'(q) > 0 and c"(q) > 0. The firm sells x units in the futures market at price f and sells the remaining q- x units in the spot market at random price š. Assume that s takes on two values, p+ ε₁ and p + E2 such that ₁ > 0> 2> -p. In other words, the random spot price š is defined by the gamble (2) <p+E1, p + E2; α > = where a € (0, 1). (a) Write down the profit gamble conditional on q and x. (b) Set up the maximization problem of an agent with utility function u(7) such that u' (T) > 0 and u" (π) <0. (c) Provide a graphical solution of the maximization problem. That is, sketch precisely the set of available gambles and illustrate the solution that maximizes the expected utility of profits. In particular, what is the opportunity cost of ₁ in terms of ₂ (via hedging)?

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a The profit gamble conditional on q and x is where qx qx fx cq and qx1 qx p 1 cq b The maximization ... View the full answer