生产者理论2.ppt

Q Q P C/Q CQ P cuts average cost at its minimum marginal cost P Q PQ Revenue P Q C/Q Revenue and Costs C/Q profits vary with Q ... Q Q Q Q Q Q Q P CQ P Maximum Profits price = marginal cost What condition holds at exactly this point?? P C/Q CQ price marginal cost P Q Q* = 0 What happens if price is low... First-order conditions if Q* 0: Price equals marginal cost Price covers average cost P = CQ (w, Q*) P 3 C(w, Q*) Q* ______ covers both the cases: Q*0 and Q*=0 ... and in general: PQ* 3 C(w, Q*) ￡ Profit maximisation can be viewed in two stages Stage 1: choose inputs to minimise cost Stage 2: choose output to maximise profit Use these to predict firms reactions Summary * The Firm: Optimisation Advanced MicroEconomics Objectives Constraints Method -Profit maximisation? - Technology; other - 2-stage optimisation Lets make a quick list of the components of a standard optimisation problem. Lets also look ahead to the way we will do it for the firm... The optimisation problem ...and quantities wi P price of input i price of output zi Q amount of input i amount of output Use the information on prices... P Q - S wi zi m i=1 Profits: P Q Revenue: S wi zi m i=1 Cost of inputs: So we get... To set up... …the objective of the firm P Q - S wi zi m i=1 - = + S wi zi m i=1 P Q The objective of the firm A simple definition of profits Choose Q and z to maximise P :=P Q - S wi zi m i=1 Q ￡ G(z) ...subject to the production constraint... Q 3 0 z 3 0 ...and some pretty obvious conditions: Optimisation: the standard approach You can’t have negative inputs You can’t have negative output Set up a Lagrangean to take care of the constraints Bang out the First Order Conditions (FOC) Check out second-order conditions sufficiency necessity Using standard methods... FOC: the First-Order Conditions L (... ) ? ?z First order conditions are used over and over in optimisation problems as we will see... L (... )=0 Th