Consider the representative consumer with preferences over the consump- tion good, c, and leisure, l described by the utility function U (c, l) = ln c + bl where b > 0. She faces a wage rate, w, in the labor market. She also receives dividend income π from the firm. In addition, she pays T units of the consumption good to the government as a lump-sum tax. (a) Set up the Lagrangian and solve for the demand of the consumption good, c, and the leisure, l. (b) Suppose that there is an increase in lump-sum taxes, T. Determine the effect of this change on c and l. (c) Assume now that π = T. Suppose that there is an increase in the wage rate, w. Determine the effect of this change on c and l. Determine the labor supply, Ns. Graph her labor supply function. Explain your results.
Consider the representative consumer with preferences over the consump- tion good, c, and leisure, l described by the utility function
U (c, l) = ln c + bl
where b > 0. She faces a wage rate, w, in the labor market. She also receives dividend income π from the firm. In addition, she pays T units of the consumption good to the government as a lump-sum tax.
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(a) Set up the Lagrangian and solve for the demand of the consumption good, c, and the leisure, l.
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(b) Suppose that there is an increase in lump-sum taxes, T. Determine the effect of this change on c and l.
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(c) Assume now that π = T. Suppose that there is an increase in the wage rate, w. Determine the effect of this change on c and l. Determine the labor supply, Ns. Graph her labor supply function. Explain your results.
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