can you please solve this question for me 7. Consider a representative consumer that has preferences over bundles of consumptiongoods c, and leisure l. The consumer's preferences satisfy the properties: more is pre-ferred to less; preference for diversity; normality. The consumer is endowed with anendowment of total hours h. Let the consumer's real wage per hour worked in terms ofthe consumption good be w. Real firm profits, which are distributed to consumers asdividends, are denoted II. The real lump-sum taxes paid by consumers to the governmentare T. Assume that II > T.(a) Derive the consumer's budget constraint and draw it on a carefully labeled dia-gram. Show the optimal choice for the representative consumer. Explain what thecondition that holds at the optimum is.(b) Suppose now that in addition the government imposes a proportional income taxT < 1 on wage income. What is the effect of the proportional income tax rate on theconsumer's choices of consumption and leisure, as well as on his welfare? Explainthe results in terms of substitution and income effects.(c) Suppose now that in (a) consumption and leisure are perfect complements and theconsumer always wants to consume two units of consumption goods for every unitof leisure. Show the consumer's optimum on a graph. Derive algebraically solutionsfor c and at the optimum and explain how they depend on lump-sum taxes.

Consumer has preference over : Consumption(c) & Leisure (l ) Total Number of hours = h Real…

Consider a representative consumer that has preferences over bundles of consumption goods c, and leisure l. The consumer's preferences satisfy the properties: more is pre- ferred to less; preference for diversity; normality. The consumer is endowed with an endowment of total hours h. Let the consumer's real wage per hour worked in terms of the consumption good be w. Real firm profits, which are distributed to consumers as dividends, are denoted II. The real lump-sum taxes paid by consumers to the government are T. Assume that II > T.

Consider a representative consumer that has preferences over bundles of consumption goods c, and leisure l. The consumer's preferences satisfy the properties: more is pre- ferred to less; preference for diversity; normality. The consumer is endowed with an endowment of total hours h. Let the consumer's real wage per hour worked in terms of the consumption good be w. Real firm profits, which are distributed to consumers as dividends, are denoted II. The real lump-sum taxes paid by consumers to the government are T. Assume that II > T.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

can you please solve this question for me

7. Consider a representative consumer that has preferences over bundles of consumption
goods c, and leisure l. The consumer's preferences satisfy the properties: more is pre-
ferred to less; preference for diversity; normality. The consumer is endowed with an
endowment of total hours h. Let the consumer's real wage per hour worked in terms of
the consumption good be w. Real firm profits, which are distributed to consumers as
dividends, are denoted II. The real lump-sum taxes paid by consumers to the government
are T. Assume that II > T.
(a) Derive the consumer's budget constraint and draw it on a carefully labeled dia-
gram. Show the optimal choice for the representative consumer. Explain what the
condition that holds at the optimum is.
(b) Suppose now that in addition the government imposes a proportional income tax
T < 1 on wage income. What is the effect of the proportional income tax rate on the
consumer's choices of consumption and leisure, as well as on his welfare? Explain
the results in terms of substitution and income effects.
(c) Suppose now that in (a) consumption and leisure are perfect complements and the
consumer always wants to consume two units of consumption goods for every unit
of leisure. Show the consumer's optimum on a graph. Derive algebraically solutions
for c and at the optimum and explain how they depend on lump-sum taxes.

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