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**Unformatted text preview: **Third degree price discrimination 2 Third degree price discrimination 3 Marginal revenue and marginal cost Graph of third degree price discrimination Another Map Profit maximization and input demands max x , l , k px- wl- rk subject to x = f ( l , k ) = min { 2 l 1 / 2 , k 1 / 2 } Supply function Get supply function by substituting input demands into the production function: x ( w , r , p ) = f ( l ( w , r , p ) , k ( w , r , p )) . Profit function Get profit function by substituting input demands and supply function into profits: π ( w , r , p ) = px ( w , r , p )- wl ( w , r , p )- rk ( w , r , p ) . Hotelling’s Lemma Corner solutions 1 Corner solution for input demands when production function is not strictly quasi-concave min { f ( l A , k A ) , f ( l B , k B ) } < f ( tl A + ( 1- t ) l B , tk A + ( 1- t ) k B ) for 0 < t < 1 and either l A 6 = l B or k A 6 = k B . 2 Corner solution for output when production function is CRTS or IRTS Cost minimization to conditional input demands min l , k wl + rk subject to x = f ( l , k ) = min { 2 l 1 / 2 , k 1 / 2 } Cost function Substitute conditional input demands into costs to get cost function. Cost function to supply function max x px- c ( w , r , x ) Short and long run ∂ l ∂ w < ∂ l k ∂ w < ∂ x ∂ p > ∂ x k ∂ p > Entry and exit...

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