lecture17full

lecture17full - Third degree price discrimination 2 Third...

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Third degree price discrimination 2

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Third degree price discrimination 3
Marginal revenue and marginal cost

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Graph of third degree price discrimination
Another Map

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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 )) .

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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

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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 }

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Cost function Substitute conditional input demands into costs to get cost function.
Cost function to supply function max x px - c ( w , r , x )

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Short and long run l w < l k w < 0 x p > x k p > 0
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