Microeconomics †Summary Essay

Linear accept curve Q = a bP plasticity E d = (Q/P)/(P/Q) = -b(P/Q)E d = -1 in the middle of require curve (up is more elastic) Total revenue and ElasticityElastic Ed -1PR (P by 15%Q by 20%)Inelastic 0 Ed -1PR (P by 15%Q by 3%)Unit elastic Ed = -1R remains the same (P by 15%Q by 15%) MR positive expansion effect (P(Q) sell of additional units) + expense reduction effect (reduces revenues because of lower determine (P/Q)/Q) 1. Monopoly maximizes reach by setting MC = MRMonopolists Markup = outlay-cost margin = Lerner index (P-MC)/P = -1/ Ed (the less elastic direct, the greater the markup over marginal cost)2. expense DiscriminationPerfect expenditure discrimination the trusty sets the price to each individual consumer equal to his willingness to payMR=P(Q)= read (without the price reduction effect), no consumer surplus,find profit from graph Two-part Tariffs a contumacious fee (= consumer surplus) + a separate per-unit price for each unit they buy (P = MC) 2 grou ps of customers with discrimination inverse demand number for individual demands MR MR=MC * without discrimination sum of not-inverse demand functions = cardinal option for aggregate demand. Other option is the rich people demand function. Compare profits to find Qagg.* max fixed payment F (enabling discrimination) = max d added to MC1 = /q1 (with discrimination) Quantity-dependent pricing one price for first X units and a cheaper price for units above step X. profit function = = Pa*Qa+Pb(Qb-Qa)-2Qb Qb includes Qa, so the additional units sold are Qb-Qa. Example P=20-Q. true offers a bar discount. Setting a price for Qa (Pa) and a price for additional units Qb-Qa (Pb). Pa=20-Qa Pb=20-Qb. =(20-Qa)Qa + (20-Qb)(Qb-Qa) -2Qb = 18Qb-Qa2 Qb2 +QaQb withhold a=-2Qa+Qb b=18-2Qb+Qa compare to 0. 2Qa=Qb. Plug into second function 18-2(2Qa)+Qa=0. So Qa=6 Qb=12 3.Cost and Production TechnologiesFixed costs avoidable not incurred if the performance level = 0 unavoidable/sunk incu rred even if production level = 0, get dressedt exist in thelong run, for the concisely run typical Efficient scale of production min AC derivative of AC = 0 MC = AC Production technologies production method is efficient it there is no other way to engender more output development the same amounts of inputs Minimization problem object function min(wL+rK), constraint subject to Q=f(K,L) express K as a function of L, Q (from production function) plug away the expression into objective function (instead of K) derive with respect to L = 0 express L (demand for labor) plug demand for labor into K function express K (demand for capital) TC=wL+rK bare(a) product ratio rule for f(K,L)=KaLb at the optimum MPL/w = MPK/r find MPL, MPK from production function find relationship between K,L using marginal product ratio rule plug K/L into production function find K/L for desired level of production for f(K,L)=aK+bL compare MPL/w, MPK/r use production factor with high marg inal value, if equal use any combination4. Perfect emulationShort run 1. Quantity rule basic condition MR = P = MC 2. Shut-down rule P(Q) AC(Q) produce MR=MC, P(Q) AC(Q) shut down, P(Q) = AC(Q) profit = 0 for two options * shut-down quantity and price min AC (derivative of AC = 0) AC=P=MC (profit = 0) * when computing AC ignore unavoidable/sunk fixed costs (not influenced by our decision) foodstuff place equilibrium multiply individual render functions (from P=MC example TC = 4q2 so MC = 8q compare to p so 8q=p so q=p/8) by number of cockeyeds = aggregate supply function Qs Qs=Qd (demand function) equilibrium price and quantity Long run profits = 0 P=AC, equilibrium MR=P=MC=ACmin * in the long run, unavoidable/sunk cost dont exist fixed costs are avoidable dish out them into account market equilibrium find individual supply function (MC=P), quantity produced by 1 cockeyed (MC=AC =price plug price into demand function total quantity demanded number of firms in the market = total quantity demanded/quantity produced by 1 firm5. Oligopolistic MarketsGame Theory Nash Equilibrium each firm is making a profit-maximizing choice given the actions of its rivals (cannot increase profit by ever-changing P or Q) best response = a firms most profitable choice given the actions of its rivals Bertrand Model setting prices at the same time 1 interactiontheoretically max joint profit when charging monopoly price (MC=MR) but undercutting prices P=MC, = 0 infinitely repeated explicit x tacit collusion (when r is not too high) Cournot Model choosing quantity (based on beliefs on the other firms production) simultaneously market price market equilibrium residual demand for firm 1 from the inverse demand function profit 1 as a function of q1, q2 derivative = 0 best response function for firm 1 same steps for firm 2 find q1, q2, market quantity price, profits Stackelberg Model choosing quantities sequentially firm 1 not on its best response fun ction higher profit, firm 2 is market equilibrium find best response function of firm 2 plug into profit function of firm 1 derivative = 0 q1, q2 (from BR2 function) price, profits