STAT0001: Economics 2 (Combined Studies) Alex Donov Department of Statistical Science University College London a.donov@ucl.ac.uk 2Outline: Term 1 Mathematics Overview and Budget Constraint Preferences and Utility Choice and Demand Revealed Preference Slutsky Equation Choice under Uncertainty Consumer Surplus Production Technology and Profit Maximisation Cost Minimisation and Cost Curves Competitive Markets 3Competitive Markets Profit Maximisation Re-Visited Perfect Competition Supply Short-Run Industry Equilibrium Long-Run Entry 4Producer’s Profit-Maximisation Problem Still assuming a price-taking firm but with the cost function from the cost-minimisation problem Assume that is a convex function of y( )yc ( )ycpy y max 5Competitive Markets Profit Maximisation Re-Visited Perfect Competition Supply Short-Run Industry Equilibrium Long-Run Entry 6Firm’s Supply Function The FONC for the firm’s profit-maximisation problem is: – Verify the SOSC: Can show that the supply function is the portion of the MC curve that lies above the AVC Furthermore, the supply function is non-decreasing in the price ( )( ) 0* = pycp ( )( ) ( ) ( ) ( )( ) 0 1 01 * * * * = = pycdp pdy dp pdy pyc ( )( ) ( )( ) 00 ** pycpyc 7Competitive Markets Profit Maximisation Re-Visited Perfect Competition Supply Short-Run Industry Equilibrium Long-Run Entry 8Aggregating Supply Suppose that you have N firms in a perfectly competitive industry Firm n solves its profit-maximisation problem assuming no influence on the market-clearing price – FONC for firm n: In equilibrium, industry supply has to equal the demand Thus, there are N+1 equations and unknowns ( ) ( )pDpy N n n = =1 * ( )( )pycp nn * = 9Market Equilibrium: Two Asymmetric Firms, Linear MC, and Linear Demand ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 14 20 , 7 20 , 7 20 10 2 7 210 2 3 210 2 210 2 ,2, 210,, 2 1 ** 2 ** 1 * * * * * * * * 2 1 ** * 2 * 121 2 222 2 111 === = = =+ = == == === = pypyp p p p p p p ppyMCC p pyppyypypFONC ppDyycyyc n n 10 Market Equilibrium: N Symmetric Firms, Linear MC, and Linear Demand ( ) ( ) ( ) ( ) ( ) ( ) ( ) NB AN py NB A py NB A p ApNB BpANp BpApyMCC ppyypFONC BpApDyyc N n nn N n n nn nnn + = + = + = =+ = = = = == = = 1 ***** * ** * 1 ** * 2 ,, , 2 1 11 Comparative Statics: N Symmetric Firms, Generic MC, and Generic Demand ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )( ) ( )( ) 0 , *** *** ***** ** *** * 1 ** ** = =+ = = = = = = dp Npdy N dp NpdD Npy dN Ndp dN Ndp dp NpdD dN Ndp dp Npdy NNpy NpDNpNy NpDNpyMCC pypyycpFONC pDnycyc N n nn nnn 12 Welfare Analysis: Two Asymmetric Firms, Linear MC, and Linear Demand ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 7 10 , 7 20 02 2 52 0 2 51 4 5max max 210,, 2 1 * 2 * 1 * 2 * 2 * 1 * 1 * 2 * 1 * 22 * 11 2* 2 * 1* 2 * 1 , 2 1 ***** 0, 2 222 2 111 * 2 * 1 * * 2 * 1 == = + = + + + + =+= === = yy y yy FONC y yy FONC ycyc yy yy ycYpYpdYYpPSCSSW ppDyycyyc yy n nn Y D yy 13 Welfare Analysis: N Symmetric Firms, Linear MC, and Linear Demand ( ) ( ) ( ) ( ) ( ) ( ) ( ) NB A y B AN B NBN y Nyy B N B AN FONC yNcy B N y B AN ycYpYpdYYpPSCSSW BpApDyyc y N n nn Y D yy nnn N + = = + = + =+= == = * * ** 2 *2* 2 * 1 ***** 0,, 2 0 2 max max , 2 1 * * ** 1 14 Competitive Markets Profit Maximisation Re-Visited Perfect Competition Supply Short-Run Industry Equilibrium Long-Run Entry 15 Long-Run Perfectly Competitive Equilibrium ( ) ( ) ( ) ( ) ( ) ( ) F FBA N FBAFN BpAFN pDNyMCC FpFONC Fy y F yyMCyAC yyMC y F yyACFyyc 2 2 2 2, * ** * * * *** 2 = = = = = = = = =+= +=
