Let's assume you've already completed the input optimization and found your company's cost function as follows: C(Y)=Y^2 + 3Y
a) Write down the firm's profit function
b) Write down the first order condition for maximization and solve for Y* = f(P)
c) Suppose that P=$9. Find Y* and show that at this level of output, marginal revenue is equal to marginal cost.
d) Calculate the firms profit at Y* and P=$9.
e) Repeat c. and d. with P=$15