Question
In: Economics
Assume an individual has a utility function of this form U(C, L) = 40 + 5(CxL)...
Assume an individual has a utility function of this form U(C, L) = 40 + 5(CxL) This utility function implies that the individual’s marginal utility of leisure is 5C and her marginal utility of consumption is 5L. The individual has an endowment of V=$40 in non-labour income and T = 18 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$2 and the wage rate for each hour of work w=$20.
(a) Calculate the rate at which the individual is willing to sacrifice an additional leisure hour when she is already working 6 hours.
(b) What is this individual’s optimal amount of consumption and leisure?
(c) Suppose that the market wage rate for each hour of work goes up from w=$20 to w=$22. Discuss how you would determine whether the substitution effect or income effect dominates in response to this wage increase. (In answering this part you do not need to do the actual calculations but you need to describe each step you would use)
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
Suppose that an individual has a utility function of the form U = Y½ where U...
Suppose that an individual has a utility function of the form U
= Y½ where U is utility and Y is income.
a) Calculate the utility level for Y values of $10,000,
$40,000, $90,000, $160,000, and $250,000 and then plot the
individual’s total utility function.
b) This individual is currently earning $90,000 but has
a 50-50 chance of earning either $40,000 or $160,000 in a new
job.
i) Calculate the expected income and utility from the
new...
Assume that a worker has the Utility Function U(C,L) = C 0.25 L0.75 “C” refers...
Assume that a worker has the Utility
Function U(C,L) = C 0.25 L0.75
“C” refers to consumption in dollars
and “L” to hours of leisure in a day. The worker has an offered
wage of $10 per hour, 20 hours available for leisure or work per
day, and $90 dollars a day from non-labour income.
a)
Find the budget constraint equation of the
individual.
b) Find
the optimal choice for the individual in terms of units of...
A individual has a utility function u(c) = √ c, where c is the individual’s consumption....
A individual has a utility function u(c) = √ c, where c is the
individual’s consumption. (The individual consumes his entire
wealth.) The individual’s wealth is $40,000 per year. However,
there is a 2% chance that he will be involved in a catastrophic
accident that will cost him $30,000.
PLEASE SHOW WORK
a. What is the individual’s utility from consumption if there is
no accident? What is his utility if there is an accident? What is
his expected utility?
b....
Suppose that the utility function is U(c, l) = c^(a) l^(1−a) where < a < 1....
Suppose that the utility function is U(c, l) = c^(a) l^(1−a)
where < a < 1. Calculate the slope of an indifference curve
for this utility function. What happens to the slope of the
indifference curve when c decreases and l increases? Explain.
Robert has utility function u(c,l) = cl over consumption, c, and leisure, l. Robert is endowed...
Robert has utility function u(c,l) = cl over consumption, c, and
leisure, l. Robert is endowed with 16 hours of leisure. Let the
price of consumption be p = 1. Robert can sell his time in the
labor market at hourly wage, w. The equilibrium we will consider
implies zero firm profits, so labor income is the only source of
income for consumers. Thus, Robert’s budget line can be written by
c + wl = 16w. Production of the consumption...
Robert has utility function u(c,l) = cl over consumption, c, and leisure, l. Robert is endowed...
Robert has utility function u(c,l) = cl over consumption, c, and
leisure, l. Robert is endowed with 16 hours of leisure. Let the
price of consumption be p = 1. Robert can sell his time in the
labor market at hourly wage, w. The equilibrium we will consider
implies zero firm profits, so labor income is the only source of
income for consumers. Thus, Robert’s budget line can be written by
c + wl = 16w. Production of the consumption...
Suppose that a representative consumer has the following utility function: U(C,L)=5ln(C)+2ln(L) and she has the budget...
Suppose that a representative consumer has the following utility
function: U(C,L)=5ln(C)+2ln(L) and she has the budget constraint
w(h-L)+pie-T. Derive the consumer's rules for consumption and
leisure (solve for consumption and leisure "demand functions" as a
function of exogenous variables).
Graph and discuss the income and substitution effects for a
consumer if her wages decreased (with labels).
Say the household has utility U (c, l) = c + log (l) and is endowed...
Say the household has utility U (c, l) = c + log (l) and is
endowed with h = 1 units of time and no units of capital. The
government has planned expenditures of G = 1. The firm's production
technology is Y = 4N.
Now assume that the government cannot finance G trough a
lump-sum tax, but has to rely on a proportional tax on income.
Solve for the value (or values) of τ that allows the government
to...
An individual has the utility function: u(c,h)= ln(c) -a/Hwhere C represents consumer spending. H...
An individual has the utility function: u(c,h)= ln(c) -
a/Hwhere C represents consumer spending. H is the amount spent on
insurance disease. The parameter α indicates whether the individual
is sick or not, such that α = 0 when the person is in good health
and α = 1 when the person is sick. The probability of getting sick
is equal to k. The individual has an income m, and has the budget
constraint C + H = m.The individual...
Jenny has preferences given by the utility function U(C; L) = C2L so that the slope...
Jenny has preferences given by the utility function U(C; L) =
C2L so that
the slope of her indi§erence curve is C : Johnny has the same
preferences 2L
wesawintheclassexample(i.e.
U(C;L)=CLsotheslopeofhisindi§erence
curve at any point is C): L
(1) Which of them has the relatively stronger preference for
consumption over leisure? Explain.
(2) They can both earn $10 per hour, they both have a non-labor
income of $300 per week and they have 110 hours per week of
non-sleeping time...
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