Consider the Model of the Firm under Price Uncertainty. In that model profit is defined as: II = X-C(X) - F, where X is output, C(X) is the variable cost function and F is the fixed cost. is the random price with distribution (p1, p2; 1, 1-1t). 1. Write the probability distribution of profits. Suppose that C(X) =(X)?; F = $10; n =1-1 = 0.5; p = $30, p2 = $40. Consider the following risky prospects: R1. Produce 10 units. R2. Produce 15 units. R3. Produce 20 units 2. Use 1 above to obtain the distribution functions of profits that correspond to the three risky prospects proposed. 3. Use the expected utility approach - without knowing the specific utility function to assess the riskiness of the proposed production plans. 4. The owner of a firm has the following utility function u(II) = (Tt)12. Calculate the expected utility of every risky prospect and rank them according to the investor's utility function. 5. The owner of a firm has the following utility function v(II) = Ln (Tt).Calculate the expected utility of every risky prospect and rank them according to the investor's utility function. 6. The owner of a firm has the following utility function w(II) = (TT)?. Calculate the expected utility of every risky prospect and rank them according to the investor's utility function. Consider the Model of the Firm under Price Uncertainty. In that model profit is defined as: II = X-C(X) - F, where X is output, C(X) is the variable cost function and F is the fixed cost. is the random price with distribution (p1, p2; 1, 1-1t). 1. Write the probability distribution of profits. Suppose that C(X) =(X)?; F = $10; n =1-1 = 0.5; p = $30, p2 = $40. Consider the following risky prospects: R1. Produce 10 units. R2. Produce 15 units. R3. Produce 20 units 2. Use 1 above to obtain the distribution functions of profits that correspond to the three risky prospects proposed. 3. Use the expected utility approach - without knowing the specific utility function to assess the riskiness of the proposed production plans. 4. The owner of a firm has the following utility function u(II) = (Tt)12. Calculate the expected utility of every risky prospect and rank them according to the investor's utility function. 5. The owner of a firm has the following utility function v(II) = Ln (Tt).Calculate the expected utility of every risky prospect and rank them according to the investor's utility function. 6. The owner of a firm has the following utility function w(II) = (TT)?. Calculate the expected utility of every risky prospect and rank them according to the investor's utility function