! Assume that output (Y) in the economy isgiven by a Cobb-Douglas productionfunction, y=zK^aN^1-a where z representstotal factor productivity, K is the fixedcapital stock, and N is labor. Utility is givenby U=In(C)+blnL, b > 0 where C isconsumption, and I denotes leisure.Government collects taxes by taxing thefirm's revenue at a flat rate of t. (After-taxrevenue for the firm is (1 – t)y). Thegovernment uses the tax to fund itsexpenditure G=Ty, and consumers do notvalue G. Assume that initially G=tY=G1 a)Household Problem: Write the equation forthe household budget constraint as afunction of leisure. Assuming that thehousehold takes the wage (w1) and profits(pie1) as given, draw a graph of thehousehold's optimization problem, with con vertical axis and I on horizontal,denoting optimal values of consumptionand leisure with subscript 1 (1). Labeleverything, including intercepts. What is theslope of the budget constraint?

The Cobb-Douglas Production function is an equation that demonstrates the link between the amount of…

Answered: Household Problem: Write the equation…

Household Problem: Write the equation for the household budget constraint as a function of leisure. Assuming that the household takes the wage (w1) and profits. (pie1) as given, draw a graph of the

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Assume that output (Y) in the economy is
given by a Cobb-Douglas production
function, y=zK^aN^1-a where z represents
total factor productivity, K is the fixed
capital stock, and N is labor. Utility is given
by U=In(C)+blnL, b > 0 where C is
consumption, and I denotes leisure.
Government collects taxes by taxing the
firm's revenue at a flat rate of t. (After-tax
revenue for the firm is (1 – t)y). The
government uses the tax to fund its
expenditure G=Ty, and consumers do not
value G. Assume that initially G=tY=G1 a)
Household Problem: Write the equation for
the household budget constraint as a
function of leisure. Assuming that the
household takes the wage (w1) and profits
(pie1) as given, draw a graph of the
household's optimization problem, with c
on vertical axis and I on horizontal,
denoting optimal values of consumption
and leisure with subscript 1 (1). Label
everything, including intercepts. What is the
slope of the budget constraint?

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