(c)(6%) Assuming the least efficient producers are active, what's the producer surplus (PS) under the price floor? What's the deadweight loss due to the price floor?

8. Consider a market of risk-averse decision makers, each with a utility function U = √I. Each decision maker has an income of $90,000, but faces the possibility of a catastrophic loss of $50,000 in income. Each decision maker can purchase an insurance policy that fully compensates her loss. This insurance policy has a cost of $11,600. Suppose each decision maker potentially has a different probability q of experiencing the loss.(6%) What is the smallest value of q so that a decision maker purchases insurance?

(a)(5%) What is the compensating variation when \( P_{x} \) increases from \( \frac{1}{3} \) to \( \frac{1}{2} \)?

(b)(5%) What is the equivalent variation when \( P_{x} \) increases from \( \frac{1}{3} \) to \( \frac{1}{2} \)?

(c)(5%) What is the income effect when \( P_{x} \) increases from \( \frac{1}{3} \) to \( \frac{1}{2} \)?

(a)(10%) What are the conditions in \( \beta \)'s to ensure that the translog cost function is homogeneous of degree one in \( w \) and \( r \)?

(b)(5%) What is the condition in \( \beta \)'s for the translog cost function to reduce to the constant elasticity cost function?

(a)(5%) Which column represents the demand side, if any?

(b)(5%) Which column represents the supply side, if any?

(c)(5%) What do you know about the cell labeled (c)?

(d)(5%) What do you know about the cell labeled (d)?[Hint for (c) and (d): provide a range, for example "the number must be smaller than -1.00," when you do not know the exact number.]

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