Consider a one period model in which a representative agent maximises the utility function: u(c,l) = lnc + 5lnl subject to the budget constraints: c = (1-t)w(1-l) + v where c is consumption and l is the amount of leisure, they enjoy out of a total of one unit of time available, t is the tax on wage earnings which pays for v in government transfer payments. A. Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? B. Solve for the maximum amount of revenue the government can raise from this tax. Hint: the tax rate will be a fraction between 0 and 1. C. In this particular example, what are the contributions of the income and substitution effects?
Consider a one period model in which a representative agent maximises the utility function:
u(c,l) = lnc + 5lnl
subject to the budget constraints:
c = (1-t)w(1-l) + v
where c is consumption and l is the amount of leisure, they enjoy out of a total of one unit of time available, t is the tax on wage earnings which pays for v in government transfer payments.
A. Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called?
B. Solve for the maximum amount of revenue the government can raise from this tax. Hint: the tax rate will be a fraction between 0 and 1.
C. In this particular example, what are the contributions of the income and substitution effects?
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