3. First and Second Welfare TheoremsThere are two goods A and B and two inputs K and L. The production functions areAKLI-aBKLYa%3DY, =The production functions display the standard properties, including constant returnsto scale.A representative houschold has utilityU(Ca, Cs)where c; is the consumption of good i. The total supply of each factor is fixedKKa + K,L = La+ Loduetion Now assume a market system.i. Households own the labor and capital, which is rented to firms. The householdfaces a budget constraintwa La + wLb +raKa+ r¿K½ > PaCa + PbCbwhere wi is the real wage paid in industry i and r; is the rental rate inindustry i. The total supply of each factor is fixed, as described above. Solvethe household's maximization problem.ii. Firms maximize profits. A firm's profits in industry A areTa = PaFa(Ka, La) – waLa – raKaand a firm's profits in industry B areTy = PoF,(Kb, Lt) – wrL – r&K,Solve the maximization problem for each firm.iii. State the equilibrium conditions assuming households and firms are price-takers.

The production functions display the standard properties, including constant returns to scale. A representative household has utility U(ca, Cs) where c; is the consumption of good i. The total supply of each factor is fixed K = Ka+K, L = La+L

The production functions display the standard properties, including constant returns to scale. A representative household has utility U(ca, Cs) where c; is the consumption of good i. The total supply of each factor is fixed K = Ka+K, L = La+L

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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