Please assist with the given problem. Provide step by step calculations for each problem.
1. The Alpha Company is a member of the lamp industry, which is perfectly competitive. The price of a lamp is $50. The firm's total cost function is:
TC = 1,000 + 20Q +5Q2
Where TC is the total cost (in dollars) and Q is hourly output.
a. What output maximizes profit?
b. What is the firm's economic profit at this output?
c. What is the firm's average cost at this output?
d. If the other firms in the lamp industry have the same cost function as this firm, is the industry in long-run equilibrium? Why or why not?