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  3. 3 a taxpayer has utility function ux l12 l...

Question: 3 a taxpayer has utility function ux l12 l...

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3. A taxpayer has utility function U(x, L)1/2 - L where L is hours of labour supply and r is consumption. The taxpayer earns a wage of $4 per hour worked (which is fixed throughout the analysis) (a) Suppose that the government imposes a proportional (percentage) tax at rate τ on labour incone, so that the taxpayers budget constraint is x = (1-7ML. Solve for the optimal labour supply (L) and consumption (2) as a function of T (b) What is the taxpayers maximized level of utility (i.e., the indirect utility function), as a function of ? (c) How much revenue, which is the tax rate T times labour income 4., or R = τ4. is raised by the tax? (Note: Use the ex|ression for the optimal labour supply from a) here; R will be a function of T)? (d) Say the government wants to maximize the amount of revenue it gcncratcs from the tax. It (des this by choosing τ such that dR/dT -0 and soving for T. Do this, and determine the revenu maximizing T and the arn()unt of revenue raised. With this tax rate, what is the maximized level of utility based on the indirect utility function you determined in part c) (this will now be an actual number)? (e) Now instead, suppose that the government imposes a fixed lump- sum tax T so that the taxpayers budget constraint is now L-T. Solve for the optimal labour supply (L) and consumption (x) as a function of T in this case. Calculate the maximized level of utility (the indirect utility function) as a function of T. (f) Say that the government chooses T so as to generate the same amount of revenue it raised in part d). What is the maximized

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