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Unformatted text preview: et (16 ) = L or alternatively, (16 L) = (meaning that Robinson sleeps 8 hours per night and this sleep time is counted as neither labour nor leisure). Max PC C w since w = the opportunity cost for Robinson. Max 8 PC (L1/2) w (16 - L) FOCL 4 PC L-1/2 + w = 0 L-1/2 = - w__ 4 PC L = __ 16PC2___ w2 Now, profit is maximized at the point where total revenue is equal to total cost (i.e. marginal profit is zero). PC C = w PC C = w (16 L) 153 Let w = 1 (labour = numeraire) PC (8 L1/2) = 16 16 PC2 8 PC (4PC) = 16 16 PC2 48 PC2 = 16 PC2 = 1 / 3 PC = 1 / Now, remember that we had L = __ 16PC2__ = 16 / 3 w2 C = 8 L1/2 C* = 8 (16 / 3)1/2 C* = 18.47520861 * = (16 16 / 3) = 32 / 3 Homework #3: How do we know that the Consumption / Leisure choice is, in fact, the one which maximized Robinson's utility? (Use L = 5.4 and L = 5.3 in your higher/lower calculations). PARETO OPTIMALITY THEORY
EQUILIBRIUM VS. OPTIMALITY Vilfredo Pareto (1848 1923) was born in Paris to an Italian father and a French mother. His professional background was in engineering. He became interested in Economics after a successful career in industry. In 1893, he was appointed as a professor of political economy (the post previously held by Leon Walras) at the Universite de Lausanne in Switzerland. In 1906 he retired to study sociology. We are concerned with Pareto Theory in the context of what it adds to Walrasian General Equilibrium analysis. Recall that Walrasian General Equilibrium theory incorporates three equilibrium concepts, namely, consumer equilibrium, producer equilibrium, and market 154 equilibrium. The key that holds these three equilibrium concepts together is the fundamental concept of market prices. The question of Walrasian Theory is  Existence of General Equilibrium: how do we ascertain that there exists an equilibrium price vector which can simultaneously satisfy the following conditions: all consumers are in equilibrium, all producers are in equilibrium, all markets are in equilibrium?  Computation of Ge...
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- Spring '10