Question

In: Economics

Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function...

Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function is given by the following equation ?(?, ?) = (? − 30)(? − 12). Luke pays 10% of his wage income as tax. Show all the steps, with definition of every new notation used in the steps.

a) Suppose that Luke’s pre-tax wage is $5/hour. Find Luke’s daily budget constraint equation and graph it. (5 pts.)

b) If Luke’s pre-tax wage is $5/hour, what is Luke’s optimal consumption, (? ∗ , ? ∗ )? (5 pts.)

c) Assume that the pre-tax wage is an unknown variable, ?. What is Luke’s leisure demand ?(?)? (5 pts.) d) What is Luke’s reservation wage, the lowest wage Luke is willing to work for? (3 pts.)

Solutions

Expert Solution

*Answer:

Given that,

U(L,C) = (C-30) (L-12)

*a)

Suppose that Luke's pre-tax wage is $5/hour. Find Luke's daily budget constraint equation and graph it.

Luke can work for 24 hours in a day, in that case he will earn $50 + $5(24) = $170, or he can leisure the whole day, in which case he consumes only $50.

Budget constraint

C = 50 + 5(24 - L)

*b)

If Luke's pre-tax wage is $5/hour, what is Luke's optimal consumption, (L*, C)?

When utility function U(L,C) = C*L. This implies that the marginal rate of substitution is C / L.

Therefore, Luke's marginal rate of substitution is:

MRS = (C-30) / (L-12).

Luke's optimal mix of consumption and leisure is found by setting MRS equal to wage ans solving for hours of leisure from given the budget constrain.

w = MRS

Putting the budget constrain equation in place of C

Thus Luke will choose 20 hours of leisure and consume 50 + 5*4 = $70 per day

*c)

Assume that the pre-tax wage is an unknown variable, w. What is Luke's leisure demand L(w)?

*d)

What is Luke's reservation wage, the lowest wage Luke is willing to work for?

The reservation wage is defined as the MRS when Luke is not working. When he is not working he leisures for 24 hours and consumes $50.

The reservation wage = $1.67

*** Please please like this answer so that I can get a small benefit. Please support me. Please help me. Thankyou***

Rahul Sunny answered 1 year ago
Next > < Previous

Related Solutions

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...
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,...
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.
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...
25) Consider the following one-period, closed-economy model. Utility function over consumption (C) and leisure (L) U(C,L)...
25) Consider the following one-period, closed-economy model. Utility function over consumption (C) and leisure (L) U(C,L) = C 1/2 L 1/2 Total hours: H = 40 Labour hours: N S = H – L Government expenditure = 30 Lump-sum tax = T Production function: Y = zN D Total factor productivity: z = 2 The representative consumer maximizes utility, the representative firm maximizes profit, and the government balances budget. Suppose there is an increase in total factor productivity, z, to...
A. In the consumption/leisure model, let the consumer’s utility function be U(C,l)=C.25+l.25. Suppose Pc=$1 and w1=$10...
A. In the consumption/leisure model, let the consumer’s utility function be U(C,l)=C.25+l.25. Suppose Pc=$1 and w1=$10 determine the optimal amount of C and L and the equation for the labor supply. B. Suppose w2=$12 determine the new optimal C and L and determine the substitution and income effects of the price change of leisure.
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...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT