Question 2
Suppose now that the regulator faces uncertainty about the cost of the firm. With probability \( \frac{1}{2} \), the cost is \( C(q)=40 q \) but with probability \( \frac{1}{2} \), the cost is \( C(q)=60 q \). That is, on average, the regulator believes that the cost is \( C(q)=50 q \).
1. Suppose that the firm's cost turns out to be \( C(q)=40 q \). What is the firm's optimal choice of price and quantity if the regulator imposes a cap of \( \bar{p}=50 \) on the price-per-unit? What is the consumer surplus in this case? Hint: with this price cap, the firm's best option is to set a uniform price as in the normal monopoly problem, but that uniform price could be above or below the per-unit price cap. If it is above, the firm is limited to charging the price cap.
