EC ON 3070INTERMEDIATE MICROECONOMICTHEORYSpring 2009, Hom ew ork 1Due Tuesda y, Jan. 27 (prior to commencem ent of the lecture)Carefully show how you derive you answer and be sure to interpret youranswer where necessary.1. Consider a market with (aggregate) demand given b yQd(p)=a − bpwhere a, b are positive constan ts and p is the price of the good. Supplyon that market is giv en b yQs(p)=c + zpwhere, again p is the price and c, z are some positiv e constants.(a) Pic k constants a, b and graph the dem and.(b) Pick constan ts c, z and depict the supply on the previous graph.(c) Is there an eq uilibrium ? If so, wha t is the qu antit y demanded andsupplied and wha t is the equilibrium price? Dem o nst rate yo u ranswer both algebraically (by solving for equilibrium price andquan tity) and graphically (by showing the point corresponding tothe equilibrium ).(d) Find inv erse demand function, p (Q) . Calculate elasticit y of de-man d at the equilibriu m point.1(e) Now increase constant a in the equation of deman d (that couldhappen if some potential buyers became ric her), so that the newdemand isˆQd(p)=ˆa − bpwhere ˆa =1.1a. Ho w does the equilibrium price change as a resultof this decrease? W ill more or less of the good be sold on thatmark et?2. A monopolist faces direct demand of Qd(p) = 1000 − 20p,whereQd(p)is quantity demanded at price p.(a) What is the inverse demand function?(b) What is the monopolist’s total revenue function?(c) Grap h the rev enue function, R(p)=Qd(p) p.(d) Find the monopolist’s c h oice of price that maxim izes total rev enue.Use both first and second order conditions. What is the highestrev e nue the monopolist can get?(e) What is the elasticity of dem and at that point?(f)
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