A monopoly faces the demand curve Q" = 30 -0.5p and has the cost function STC = Q2 + 100. a. Find the profit-maximizing output and price and determine the level of profit. b. Determine the elasticity of demand at the profit-maximizing output. c. Assume a tax, 7, on each unit of output. Find the profit-maximizing level of output, in terms of 7. How will output change with a change in T. d. What level of tax, T, should a government choose if it wishes to extract the maxi- mum tax revenue from this monopoly