Let the demand function be p = 60 2q, where p is the price the firm receives if it sells quantity q of output. The firm's cost function is given by C (y) =

1/2Q^2.

1. Now, suppose the government impose a sales tax (NOT profit tax) of 20% on this market. Hence, if the firm produces quantity q of output, the price paid by consumers is p = 60 2q, but the price received by the firm is 0.8p = 0.8 (60 2q), where the 0.8 appears because the firm gets to keep only 80% of the purchase price, paying the remaining twenty percent to the government in taxes. Find the profit maximizing quantity of output for the firm and the government revenue

Suppose the government switches to a quantity tax of $t to get the same revenue as in (a). What would be the tax value t?