2. Say the government levies a linear tax at rate t on all reported tax- able...
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2. Say the government levies a linear tax at rate t on all reported tax- able income. A representative agent decides on her labour supply (L) and how much income to shelter from taxation (e) through tax plan- ning (she pays no taxes on sheltered income). Tax planning is costly, however the cost is g(e), where g is increasing and convex in e (i.e., increases at an increasing rate). The agent's taxable income is thus TI = wL-e, where w is the wage rate, L is labour supply and e is the amount of tax sheltered income. The representative agent's budget constraint is C (1 t)TI + e, where C is consumption and TI is taxable income as given above. The agent's utility is additive and quasi-linear in consumption: U(c, e, L) = C-g(e)a(L), where a(L) is the disutility of working. (a) Substitute the budget constraint into the utility function for C to express the individual's unconstrained maximization problem in terms of L and e. Determine the optimizing conditions with respect to e and L and interpret them. = 2 Write down the resulting indirect utility function, denoted V. (HINT: Of course you can't solve explicitly for the IUF because you do not have an explicit functional form for the utility func- tion; rather indicate generally how the indirect utility function is determined and show what it is a function of). Use the envelope theorem to determine dv/dt. (b) Social welfare is given by the sum of the representative agent's welfare, represented by the indirect utility function V, and tax revenue: W = VtTI. The government is interested in de- termining the welfare cost of a small increase in the tax rate t, dW/dt. = An estimated parameter is said to be a sufficient statistic if that parameter provides all of the information you need to calculate the desired effect. Show that the elasticity of taxable income ( (dTI/dt) (t/TI)) is a sufficient statistic for determining the welfare cost of an increase in the tax rate. 2. Say the government levies a linear tax at rate t on all reported tax- able income. A representative agent decides on her labour supply (L) and how much income to shelter from taxation (e) through tax plan- ning (she pays no taxes on sheltered income). Tax planning is costly, however the cost is g(e), where g is increasing and convex in e (i.e., increases at an increasing rate). The agent's taxable income is thus TI = wL-e, where w is the wage rate, L is labour supply and e is the amount of tax sheltered income. The representative agent's budget constraint is C (1 t)TI + e, where C is consumption and TI is taxable income as given above. The agent's utility is additive and quasi-linear in consumption: U(c, e, L) = C-g(e)a(L), where a(L) is the disutility of working. (a) Substitute the budget constraint into the utility function for C to express the individual's unconstrained maximization problem in terms of L and e. Determine the optimizing conditions with respect to e and L and interpret them. = 2 Write down the resulting indirect utility function, denoted V. (HINT: Of course you can't solve explicitly for the IUF because you do not have an explicit functional form for the utility func- tion; rather indicate generally how the indirect utility function is determined and show what it is a function of). Use the envelope theorem to determine dv/dt. (b) Social welfare is given by the sum of the representative agent's welfare, represented by the indirect utility function V, and tax revenue: W = VtTI. The government is interested in de- termining the welfare cost of a small increase in the tax rate t, dW/dt. = An estimated parameter is said to be a sufficient statistic if that parameter provides all of the information you need to calculate the desired effect. Show that the elasticity of taxable income ( (dTI/dt) (t/TI)) is a sufficient statistic for determining the welfare cost of an increase in the tax rate.
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ANSWER a Substituting the budget constraint into the utility function we get the agents unconstraine... View the full answer
Related Book For
Intermediate Accounting
ISBN: 978-0324592375
17th Edition
Authors: James D. Stice, Earl K. Stice, Fred Skousen
Posted Date:
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