Perfect competition

The market demand for a type of carpet known as KR-3 has been estimated asP=40-0.25Q, where P is the price ($/yard) and Q is the market-wide rate of sales (hundreds of yards per month).The firm output is denoted as "q".The market supply is expressed asP=5.0+0.05Q.A typical firm in this market has marginal and total cost functions: MC=-5+4q and TC = 100-5q+2q².

a.Determine the equilibrium market output (Q*, hundreds of yards per month) and price, using algebra.Explain each step you make in your calculation.

b.Find the optimal output (q* per month) for a typical firm in the industry, explaining your reasoning.

c.Calculate fixed costs for the firm and variable costs at the profit-maximizing level of output.

d.Does the typical firm lose money or earn a positive profit?Calculate the amount.