Jack is the only seller of pizza in the market. Jack's production function is TC= 0.5Q+15. The market demand for pizza is P=20.5-0.5Q.

a) Calculate the profit-maximizing price and quantity for Jack's pizza business. Illustrate the market equilibrium with a proper diagram.

b) Evaluate the profit of Jack's pizza store. Compare the quantity of pizza sold by Jack with the equilibrium quantity resulting from a perfectly competitive pizza market. Estimate the size of market efficiency loss (or gain) caused by Jack's pizza business.

c) Government considers that eating pizza is unhealthy and is planning to impose a $5 tax on the seller for each pizza sold in the market. Evaluate the changes in quantity demanded and profit for Jack's pizza store. Discuss whether Jack will remain or leave the market after the tax.