Answered: Consider a one period model in which a…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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 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.

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