題組內容

4. (20 %)

Consider a firm whose CEO's compensation equals a fraction λ of the firm's operating profit. The CEO is risk-averse and has utility U(W)=ln (W), where W is the compensation. The firm's production function is y=θ√k, where k≥0 is the capital input and θ is a random productivity shock with

Probability(θ=2)=1/2, Probability(θ=1)=1/2.

(b) Compare the optimal capital input under uncertainty with the risk-neutral benchmark case. Is the optimal capital choice under uncertainty higher or lower than in the deterministic case? Explain your result using both mathematical reasoning and economic intuition. (10%)