1. Take into account the general public good mannequin of the 2 flatmates and TV with the preliminary wealths w1 =w2 = 100.(a) Suppose the TV itself is the general public good, in order that, G = 1 means TV is supplied andG = zero means TV shouldn't be supplied. The price of the TV is c = 75 and the utility functionsare such that, for every i = 1, 2: U i(xi, G) = xi if G = 1; and U i(xi, G) = xi/2 ifG = zero. Discover the reservation worth of every particular person. Is it optimum to offer the TV?(b) As a substitute of (a), suppose the standard of the TV is the general public good with the price operate ofTV high quality given by C(G) = G2. Additionally, suppose the utility operate of every individuali = 1,2 is: U i(xi, G) = xiG. Present that the optimum quantity of the general public good isthe identical in each Pareto environment friendly allocation. What is that this quantity? Will the optimalamount of the general public good change if the preliminary wealths of the 2 people change?2. A monopolist sells in two markets. The inverse demand curves within the two marketsare P1(y1) = 75- (y1/2) and P2(y2) = 100- y2, the place yi is the amount in market i = 1, 2.The monopolistâs whole value operate is given by C(Y ) = 50+2Y +Y 2, the place Y is the totaloutput of the monopolist.(a) Suppose, as a result of it's not possible for anybody aside from the monopolist to move thegood between the 2 markets, the monopolist is ready to worth discriminate betweenthe two markets. How a lot will the revenue maximizing monopolist promote in every of thetwo markets and at what costs?(b) Suppose it's now potential for anybody to move the nice from one market to theother at zero transportation value. Discover the revenue maximizing monopolistâs optimalprice and the portions it should promote within the two markets at this worth.three. T plc operates the one public transport system within the city of ABC. T plc can solely chargea single uniform worth of $F per journey. ABC has 1000 similar residents, who every takesX = 40 - 5F journeys per yr if the value per journey is $F . T plc has a continuing marginal costof $zero.four per journey.(a) If T plc shouldn't be allowed to apply two half tariff pricing, discover the monopoly worth of atrip and the overall variety of journeys it should promote per yr.(b) If T plc is allowed to apply two half tariff pricing by charging an annual membershipfee to every citizen along with the uniform worth $F per journey, discover the optimalmembership price, the uniform worth per journey and the variety of journeys every citizen willbuy per yr.(c) Calculate T plcâs annual income in (a) and (b).
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