QuestionConsider an economy with the representative consumer, representative firm, and government. Suppose that . The consumer s preferences over the consumption good and leisure are given by the utility function . Let . The firm's production function is . Suppose that the government imposes a proportional income tax on the representative consumer. The government uses the tax revenue to finance its expenditures as well as to give give each consumer a lump-sum social security transfer . There are no lump-sum taxes. That is, the consumer's budget constraint is . (a) (5 points) Write down the consumer's optimality condition. (b) (5 points) Set up the firm's optimization problem. What is the equilibrium wage rate equal to? What are the firm's profits equal to? (c) (10 points) Using your answers to parts (a) and (b) solve the consumer's problem to find the labor supply as a function of t. Take into account that the worker's labor supply cannot be lower than 0 ! (d) (10 points) Use your answer to part (c) to derive an expression for the government tax revenue as a function of the tax. Using Excel, plot the tax base (labor income) and the tax revenue (Laffer curve) against a grid of the tax rate . (e) (5 points) Provide an intuitive explanation for the shape of the Laffer curve that you plotted in part (d). In particular discuss the effects of the tax rate on the tax revenue through its effect on the different components of the tax revenue The Consumers Preferences Over The Consumption Assignment Paper.
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- Explanation for step 4
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