Question
In: Economics
Cindy gains utility from consumption C and leisure L. The most leisure she can consume in...
Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 80 hours. Her utility function is: U(C, L) = C(1/3) × L(2/3).
a) Derive Cindy’s marginal rate of substitution (MRS). Suppose Cindy receives $800 each week from her grandmother––regardless of how much Cindy works. What is Cindy’s reservation wage?
b) Suppose Cindy’s wage rate is $30 per hour. Write down Cindy’s
budget line (including $800 received from her grandmother). Will
Cindy work? If Cindy works, how many hours does she work?
Solutions
Rahul Sunny answered 7 months agoRelated Solutions
Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = min(C,2L) This utility...
Shelly’s preferences for consumption and leisure can be
expressed as U(C, L) = min(C,2L) This utility function implies that
Shelly views consumption and leisure as compliments. There are 110
(non-sleeping) hours in the week available to split between work
and leisure. Shelly earns $10 per hour after taxes. She also
receives $320 worth of welfare benefits each week regardless of how
much she works.
a) Graph Shelly’s budget line.
b) Find Shelly’s optimal amount of consumption and leisure.
c) What...
Phil’s utility for consumption and leisure can be expressed as:U(C, L) = C1/3L a. Find the...
Phil’s utility for consumption and leisure can be expressed
as:U(C, L) = C1/3L
a. Find the expression for Phil’s marginal rate of substitution
between leisure and consumption, as a function of C and L.
b. What does Phil’s utility function tell us about his relative
preference between consumption and leisure?
c. When L = 100 and C = 500, how much would Phil be willing to
pay for an additional hour of leisure? How about when L=50 and C =...
8、Assume that utility depends on consumption c and leisure l , U(c,l) . (a) Define reservation...
8、Assume that utility depends on consumption c and leisure l ,
U(c,l) .
(a) Define reservation wage.
(b) “The reservation wage increases with (i) non-labor income,
(ii) fixed monetary costs of work, (iii) fixed time costs of work,
and (iv) the price of consumption.” Prove or disprove each of these
four claims.
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...
Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = (C – 100) (L – 40).
Shelly’s preferences for consumption and leisure can be
expressed as U(C, L) = (C – 100) (L – 40). This utility function
implies that Shelly’s marginal utility of leisure is C – 100 and
her marginal utility of consumption is L – 40. There are 110
(non-sleeping) hours in the week available to split between work
and leisure. Shelly earns $10 per hour after taxes. She also
receives $320 worth of welfare benefits each week regardless of how
much...
Consider an individual with utility function c^αl^1−α, where c is consumption, l is leisure, and α...
Consider an individual with utility function c^αl^1−α, where c
is consumption, l is leisure, and α ∈ (0, 1). The individual is
endowed with R units of nonlabor income and T units of time. The
individual earns wage w for each unit of time worked. The price of
a unit of consumption is p.
(a) What is the budget constraint for this individual?
(b) What is the price of leisure?
(c) Set up the appropriate Lagrangian for this agent’s
problem....
Question 1: Given the following utility function: (U=Utility, l=leisure, c=consumption) U = 2l + 3c and...
Question 1:
Given the following utility function: (U=Utility, l=leisure,
c=consumption)
U = 2l + 3c
and production function: (Y=Output, N or Ns=Labour or Labour
Supply)
Y = 30N1/2
If h = 100 and G =10 (h=Hours of labour, G=Government spending).
Find the equilibrium levels of the real wage (w), consumption (c),
leisure (l), and output (Y).
Question 2: (Continuting from question 1)
a, Find the relationship between total tax revenue and the tax
rate if G = tWN. (G=Government spending,...
Question 1: Given the following utility function: (U=Utility, l=leisure, c=consumption) U = 2l + 3c and...
Question 1: Given the following utility function: (U=Utility,
l=leisure, c=consumption) U = 2l + 3c and production function:
(Y=Output, N or Ns=Labour or Labour Supply) Y = 30N1/2 If h = 100
and G =10 (h=Hours of labour, G=Government spending). Find the
equilibrium levels of the real wage (w), consumption (c), leisure
(l), and output (Y). Question 2: (Continuting from question 1) a,
Find the relationship between total tax revenue and the tax rate if
G = tWN. (G=Government spending,...
2-6. Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = (C -...
2-6. Shelly’s preferences for consumption and leisure can be
expressed as U(C, L) = (C - 100) × (L - 40) This utility function
implies that Shelly’s marginal utility of leisure is C - 200 and
her marginal utility of consumption is L- 40. There are 110
(non-sleeping) hours in the week available to split between work
and leisure. Shelly earns $10 per hour after taxes. She also
receives $320 worth of welfare benefits each week regardless of how
much...
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