A competitive firm sells its product at a price of $0.10 per unit. Its total and marginal cost functions are: TC = 5 - 0.5Q + 0.001Q2 MC =-0.5 + 0.002Q where TC is total cost ($) and Q is output rate (units per time period) a. Determine the output rate that maximizes profit or minimizes losses in the short term What is firm's profit at this optimum level? b. If input prices increase and cause the cost functions to become TC = 5 -0.10Q + 0.002Q2 MC =-0.10 + 0.004Q. what will the new equilibrium output rate be? Explain what happened to the profit maximizing output rate when input prices were increased. What is firm 's profit