##### Assume the market demand curve faced by a monopolist
QUESTION 1Assume the market demand curve confronted by a monopolist isQ D =500 - 10 P,and itsshort-run complete value operate is SRTC (Q) =25 +2Q.(a)(b)(c)(d)(e)Derive the inverse demand curve for the monopolist.Utilizing the outcome obtained partly (a), derive the monopolistâs complete revenuecurve as a operate of Q. Compute the corresponding marginal revenuefunction.Compute the firmâs quick run marginal value curve.Utilizing the outcomes obtained partly (b) and half (c), derive the monopolistâsshort-run profit-maximizing stage of output.Decide the value charged by the profit-maximizing monopolist and theamount of revenue earned.QUESTION 2Consider a broking agency that provides consulting companies. The corresponding demand3Q 2 Q 3relation and value capabilities are four P +Q - 16 =zero and TC (Q) =four +2Q + ,10 20respectively.(a)(b)(c)Derive the first-order situation for the companies revenue maximization. Decide theprofit maximizing stage of Q.Confirm that, on the level of most revenue that the second-order sufficientcondition holds.Test that marginal income is the same as marginal value on the profit-maximizinglevel of output decided in (b).QUESTION 3A firmâs manufacturing operate is given byQ =L2 e - zero.01L .Discover the worth of L which maximizes the typical product of labour. Make sure you havefound the worth of L that maximizes the typical product.QUESTION 4A agency produces three productsâleather-based, cardboard and stringâdenoted y1 , y2 andy3 , respectively. The corresponding complete income operate has the form2TR =5 +75 y1 - 2 y12 +eight y2 - Â½ y1 y2 +four y3 .At what mixture of outputs will the marginal revenues of all three merchandise besimultaneously equal zero?