Consider the Model of the Firm under Price Uncertainty. In that model profit is defined as: = p~ X - C(X) - F, where X is output, C(X) is the variable cost function and F is the fixed cost. p~ is the random price with distribution(p₁, p₂;, 1-).

1.Write the probability distribution of profits.

Suppose that C(X) = (X)²;F = $10; = 1 - = 0.5; p₁ = $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() = ()^1/2. 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() = ln().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() = ()².Calculate the expected utility of every risky prospect and rank them according to the investor's utility function.