201Lecture42006Small - Economics 201BSecond Half Lecture 4...

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Economics 201B–Second Half Lecture 4 The Robinson Crusoe Model: Simplest Model Incorporating Production 1consumer 1 frm, owned by the consumer Both the consumer and frm act as price-takers (silly in this model, but it shows how equilibrium operates) 2 goods: Leisure x 1 , endowment ¯ L (24 hours per day) Consumption goood x 2 bananas, endowment = 0 p : price oF bananas w : wage rate = price oF labor Production Function f ( z ): z units oF labor produces f ( z ) bananas. We assume f is strictly concave; frst gather low-hanging bananas, then start climbing trees to gather, then tend plants to increase yield ±irm’s proft: pf ( z ) wz ; frm maximizes proft, taking prices as given Labor demand z ( p, w ) Output q ( p, w )= f ( z ( p, w )) Proft Π( p, w pq ( p, w ) ( p, w ) 1
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Consumer owns frm, so receives the proft. Crusoe’s budget constraint is px 2 w ( ¯ L x 1 )+Π( p, w ) Walrasian equilibrium prices are ( p ,w ) such that markets clear: x 2 ( p )= q ( p ) (banana market) z ( p ¯ L x 1 ( p )( labormarket) In the previous diagram showing the frm’s problem, lines perpendicular to the price vector ( w, p ) (note this is labelled incorrectly as ( p, w ) in MWG) are isoproft lines. Any two points on a given isoproft line yield the same proft; this is true whether or not the point on the isoproft line is a Feasible production. In particular, iF we consider the isoproft line through the frm’s proft-maximizing point
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This note was uploaded on 08/01/2008 for the course ECON 201B taught by Professor Anderson during the Spring '06 term at University of California, Berkeley.

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201Lecture42006Small - Economics 201BSecond Half Lecture 4...

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