Is the competitive equilibrium of this economy Pareto optimal? If yes or no, explain why. Yes. The first welfare theorem ensures the Pareto optimality of the competitive equilibrium. No. Because in this economy, MRS₁¸c < MRT₁¸c holds, which violates the Pareto optimality condition. No. Because in this economy, MRS₁,c > MRT₁,c holds, which violates the Pareto optimality condition. Neither yes nor no. We need more information to determine whether the competitive equilibrium is Pareto efficient. Consider the decisions of a representative consumer whose preferences are given by: u(C,1) = In C+ Inl where C is the quantity of consumption and 1 is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the labor supply). Further, consumer take wages as given and obtain after-tax labor income that is equal to w(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint is given by C = w(1 − t)(1 − 1) + π where is the real dividend income received from the representative firm (i.e. firm profits).
Is the competitive equilibrium of this economy Pareto optimal? If yes or no, explain why. Yes. The first welfare theorem ensures the Pareto optimality of the competitive equilibrium. No. Because in this economy, MRS₁¸c < MRT₁¸c holds, which violates the Pareto optimality condition. No. Because in this economy, MRS₁,c > MRT₁,c holds, which violates the Pareto optimality condition. Neither yes nor no. We need more information to determine whether the competitive equilibrium is Pareto efficient. Consider the decisions of a representative consumer whose preferences are given by: u(C,1) = In C+ Inl where C is the quantity of consumption and 1 is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the labor supply). Further, consumer take wages as given and obtain after-tax labor income that is equal to w(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint is given by C = w(1 − t)(1 − 1) + π where is the real dividend income received from the representative firm (i.e. firm profits).
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.1P
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Transcribed Image Text:Is the competitive equilibrium of this economy Pareto optimal? If yes or no, explain why.
Yes. The first welfare theorem ensures the Pareto optimality of the competitive equilibrium.
No. Because in this economy, MRS₁¸c < MRT₁¸c holds, which violates the Pareto optimality
condition.
No. Because in this economy, MRS₁,c > MRT₁,c holds, which violates the Pareto optimality
condition.
Neither yes nor no. We need more information to determine whether the competitive
equilibrium is Pareto efficient.
Transcribed Image Text:Consider the decisions of a representative consumer whose preferences are given by:
u(C,1) = In C+ Inl
where C is the quantity of consumption and 1 is the quantity of leisure.
The consumer faces two constraints.
The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the labor
supply). Further, consumer take wages as given and obtain after-tax labor income that is equal to
w(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint is
given by
C = w(1 − t)(1 − 1) + π
where is the real dividend income received from the representative firm (i.e. firm profits).
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