5. Consider a perfectly competitive firm choosing a profit-maximizing level of output. However, there is uncertainty surrounding the market price, P, of their good, generating some uncertainty. The firm's cost function is given by C(Q) = 10 +20 + 402. There is 60% chance that the market price is $42-otherwise a relatively low price of $22 is realized. (Hint: the firm's marginal cost is given by: MC(Q) = 2 +8Q) a) Calculate the firm's profit maximizing level of output under this scenario. What are the firm's expected profits? Will that level of profits ever be realized? b) Suppose the firm can hire an outside consulting firm to provide an improved understanding of the perspective prices. They provide a perfect forecast. How much would our firm be willing to pay for the consulting firm's forecast, i.e. for their information on the future market price?