Assume an economy consists of two agents, a and b. Individual a has available 1 unit of time which he divides between leisure ra and labor ℓa . Likewise, individual b has available 1 unit of time which he divides between leisure rb and labor ℓb. Commodity x is produced by one competitive firm according to the production function: x=√L , where L denotes labor hired. The firm is fully owned by agent a. The utility function of the two individuals are: u(xa,ra)=xara and u(xb,rb)=xbrb . Taking the price of labor as the numéraire (i.e. w=1), find the competitive equilibrium for this economy.
Assume an economy consists of two agents, a and b. Individual a has available 1 unit of time which he divides between leisure ra and labor ℓa . Likewise, individual b has available 1 unit of time which he divides between leisure rb and labor ℓb. Commodity x is produced by one competitive firm according to the production function: x=√L , where L denotes labor hired. The firm is fully owned by agent a. The utility function of the two individuals are: u(xa,ra)=xara and u(xb,rb)=xbrb . Taking the price of labor as the numéraire (i.e. w=1), find the competitive equilibrium for this economy.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Assume an economy consists of two agents, a and b. Individual a has available 1 unit of time which he divides between leisure ra and labor ℓa . Likewise, individual b has available 1 unit of time which he divides between leisure rb and labor ℓb. Commodity x is produced by one competitive firm according to the production function: x=√L , where L denotes labor hired. The firm is fully owned by agent a. The utility function of the two individuals are: u(xa,ra)=xara and u(xb,rb)=xbrb . Taking the price of labor as the numéraire (i.e. w=1), find the competitive equilibrium for this economy.
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