Consider a one period model in which a representative agent maximises the utility function: U(c,l) Inc+ 5lnl subject to the budget constraints: c = (1-t)w(1-1) + v where c is consumption and 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) Solve for first order conditions of the representative agent. b) Write down the market clearing condition (resource constraint) for the aggregate economy. c) Solve for equilibrium consumption and labour choices. d) Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? e) 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.

Consider a one period model in which a representative agent maximises the utility function: U(c,l) Inc+ 5lnl subject to the budget constraints: c = (1-t)w(1-1) + v where c is consumption and 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) Solve for first order conditions of the representative agent. b) Write down the market clearing condition (resource constraint) for the aggregate economy. c) Solve for equilibrium consumption and labour choices. d) Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? e) 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.

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Chapter1: Making Economics Decisions

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

Consider a one period model in which a representative agent maximises the utility function:
U(c,l) Inc + 5lnl
subject to the budget constraints:
c = (1-t)w(1-1) + V
where c is consumption and 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) Solve for first order conditions of the representative agent.
b) Write down the market clearing condition (resource constraint) for the aggregate
economy.
c) Solve for equilibrium consumption and labour choices.
d) Derive the equation that determines how much revenue the government will receive
for a given rate of tax t. What is this relationship called?
e) 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.
f) In general, what explains the shape of the Laffer curve?
g) In this particular example, what are the contributions of the income and substitution
effects?

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