1. The demand for a firm's product is Q(P)=10-√p. The firm's cost production is C(Q)=73Q - 20Q^2 +2Q^3
(a) For what value of Q does the cost function exhibit economies or diseconomies of scale?
(b) Compute MC' and MR', the derivatives of the MC and MR functions. Is the global second order condition useful for solve this firm's profit-maximization problem.
(c) Compute the Firm's profit- Maximizing price and quantity.
2.The FOC(first order condition) and local SOC(second order condition) for the firms optimization problem can be used to prove the Law of Supply, meaning exactly: if the firm supplies a a positive quantity at the current market price, then at a higher price it will supply a larger quantity. Without doing any additional mathematics, show that a violation of the Law of Supply would imply a contradiction of the local SOC. You can assume that the firm's marginal cost function is differentiable.