Posted: February 8th, 2019

Assume the market demand curve faced by a monopolist

QUESTION 1Assume the market demand curve faced by a monopolist isQ D =500 – 10 P,and itsshort-run total cost function is SRTC (Q) =25 +2Q.(a)(b)(c)(d)(e)Derive the inverse demand curve for the monopolist.Using the result obtained in part (a), derive the monopolist’s total revenuecurve as a function of Q. Compute the corresponding marginal revenuefunction.Compute the firm’s short run marginal cost curve.Using the results obtained in part (b) and part (c), derive the monopolist’sshort-run profit-maximizing level of output.Determine the price charged by the profit-maximizing monopolist and theamount of profit earned.QUESTION 2Consider a broking firm that supplies consulting services. The corresponding demand3Q 2 Q 3relation and cost functions are 4 P +Q – 16 =0 and TC (Q) =4 +2Q + ,10 20respectively.(a)(b)(c)Derive the first-order condition for the firms profit maximization. Determine theprofit maximizing level of Q.Verify that, at the point of maximum profit that the second-order sufficientcondition holds.Check that marginal revenue is equal to marginal cost at the profit-maximizinglevel of output determined in (b).QUESTION 3A firm’s production function is given byQ =L2 e – 0.01L .Find the value of L which maximizes the average product of labour. Ensure you havefound the value of L that maximizes the average product.QUESTION 4A firm produces three products—leather, cardboard and string—denoted y1 , y2 andy3 , respectively. The corresponding total revenue function has the form2TR =5 +75 y1 – 2 y12 +8 y2 – ½ y1 y2 +4 y3 .At what combination of outputs will the marginal revenues of all three products besimultaneously equal zero?