# 1501

A monopolist faces a market demand curve given by Q = 70 – P The monopolist’s marginal revenue function is given by MR = 70 – 2Q a) Assume that the monopolist has a cost structure where total costs are described by TC = 0.25Q2 -5Q+300 and marginal cost is given by MC = 0.5Q – 5 what output level will the monopolist choose in order to maximize profits? What is the price at this output level? What are the monopolist’s profit? b) Draw the demand curve, AC and MC curve on the graph. Clearly show the equilibrium price,output and monopolist’s profit. c) Assume now that a second cost structure explais the monopolist’s position, with total costs given by and marginal cost is given by TC = 0.01Q3 -Q2 +45Q+100 MC =0.03Q2 -2Q+45 Again, calculate the monopolist’s price-quantity combination that maximizes profits. What will profits be? (Hint: set MC=MR as usual and use the quadratic formula or simple factoring to solve the equation for Q.)