3. Suppose that a monopoly faces a constant elasticitv inverse demand curve: p=5a'- '13} Here 111 is the price at 1which quantity q of the monopolv's output will he demanded. The monopoly,r produces output at constant marginal met 3 per unit of output. Xote that this means that hath average and marginal 01st are equal to 3, and the total cost of producing output at is liq. 3. Calculate prot maximizing price and cost for the monopoly. b. Show that if the government imposes a specic tax of T = l on each unit of the monopolv's output._ the rm will raise its price by more than T = l. c. Suppose that the government instead imposes an ad tlalorem tax at rate t. Calculate the price received by the monopolv in this case (to. nd the prot maximizing choice of a5 2 13:1]. Ev ho'il.r much does the price paid by consumers {pp} rise {relative to the notax casel part a} as a result of the tax