Mathematical Problem: Competitive Firm Decisions. Suppose a perfectly competitive firm experiences total cost (TC) and marginal cost (MC) according to the following equations, where Q is the quantity produced (output). The cost equations include both explicit and implicit costs.
TC = $4,000 + $5Q + $0.1Q2
MC = ?TC/?Q = $5 + $0.2Q
a. Calculate the profit-maximizing short run output and economic profit if the price the firm takes is $55.
b. Calculate the profit-maximizing short run output and economic profit if the taken price rises to $65.
c. In the long run, calculate the price, output, and economic profit. Explain what this level of profit means economically.