Question

Tom has preferences over consumption and leisure of the following form: U = ln(c1)+ 2 ln(l)+βln(c2),...

Tom has preferences over consumption and leisure of the following form: U = ln(c1)+ 2 ln(l)+βln(c2), where ct denotes the stream of consumption in period t and l, hours of leisure. He can choose to work only when he is young. If he works an hour, he can earn 10 dollars (he can work up to 100 hours). He can also use savings to smooth consumption over time, and if he saves, he will earn an interest rate of 10% per period. Suppose also that he values the future and the present equally, i.e. β = 1. (Remember the marginal utility of ln(c) is 1/c and marginal utility of leisure is given by 2/3l).
(a) Draw a standard indifference curve on the consumption today and leisure set. What is
the slope of the indifference curve?
(b) Draw a standard indifference curve on the consumption today and consumption tomor- row set. What is the slope of the indifference curve?
(c) Write down the budget constraint in the first period.
(d) Write down the budget constraint in the second period.
(e) Derive the lifetime budget constraint.
(f) Draw the lifetime budget constraint on the consumption today and leisure set. What is the slope of the budget line?
(g) Draw the lifetime budget constraint on the consumption today and consumption to- morrow set. What is the slope of the budget line?
(h) Find Tom’s optimal consumption in each period (c∗1, l∗ and c∗2) and optimal saving rate?
Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose Tom has a utility function U=C*L C= consumption L= hours of leisure Tom has 100...
Suppose Tom has a utility function U=C*L C= consumption L= hours of leisure Tom has 100 hours to divide between work and leisure per week wage is $20/hr 1. Write down budget constraint in terms of consumption and hours of work 2.Tom make decisions on hours of work, leisure and consumption to max. utility. Explain why we can collapse this problem to one in which he chooses hours of leisure only 3. Find optimal hours of work and total consumption...
Suppose preferences for consumption and leisure are: u(c, l) = ln(c) + θ ln(l) and households...
Suppose preferences for consumption and leisure are: u(c, l) = ln(c) + θ ln(l) and households solve: max c,l u(c, l) s.t. c=w(1−τ)(1−l)+T Now suppose that in both Europe and the US we have: θ = 1.54 w=1 but in the US we have: τ = 0.34 T = 0.102 while in Europe we have: τ = 0.53 T = 0.124 Compute the amount of leisure and consumption chosen in the US and Europe. Use the parameters given for each...
Hira has the utility function U(c1; c2) = c11/2 +2c21/2 where c1 is her consumption in...
Hira has the utility function U(c1; c2) = c11/2 +2c21/2 where c1 is her consumption in period 1 and c2 is her consumption in period 2. She will earn 100 units in period 1 and 100 units in period 2. She can borrow or lend at an interest rate of 10%. Write an equation that describes Hira’s budget. What is the MRS for the utility function between c1 and c2? Now assume that she can save at the interest rate...
Let Jane's Utility function be given by: U=100 x ln(C) + 50 x ln(L) where C...
Let Jane's Utility function be given by: U=100 x ln(C) + 50 x ln(L) where C is consumption (in dollars) per year and L is hours of leisure per year. Jane can make $15 per hour and can work up to 2,000 hours per year. a. set up the maximization problem, showing the budget constraint. b. How many hours will Jane want to work per year
Tom faces a labor supply decision. His well-behaved preferences over the two goods, L (leisure) and...
Tom faces a labor supply decision. His well-behaved preferences over the two goods, L (leisure) and C (consumption) can be represented by u = 4√L + C. He can choose how many hours to work at the wage rate w per hour and has no non-labor income. The price per unit of consumption is p, and his total free time is T hours. Use the tangency method to find Tom’s demand functions for leisure and consumption. In terms of parameters...
Suppose u=u(C,L)=4/5 ln⁡(C)+1/5 ln⁡(L), where C = consumption goods, L = the number of days taken...
Suppose u=u(C,L)=4/5 ln⁡(C)+1/5 ln⁡(L), where C = consumption goods, L = the number of days taken for leisure such that L=365-N, where N = the number of days worked at the nominal daily wage rate of $W. The government collects tax on wage income at the marginal rate of t%. The nominal price of consumption goods is $P. Further assume that the consumer-worker is endowed with $a of cash gift. a) Write down the consumer-worker's budget constraint. b) Write down...
Consider a consumer who has preferences over consumption (x) and leisure (L) represented by u(L, x)...
Consider a consumer who has preferences over consumption (x) and leisure (L) represented by u(L, x) = 10 ln L + 5 ln x. The consumer has 24 hours in the day (T = 24) to divide between work and leisure. The consumer can choose however many hours they want to work. For each hour of work they are paid a wage given by w = 10. Consumption (x) costs 1 per unit. (a) Initially suppose that the consumer has...
Suppose that the consumer’s preferences are given by U(c,l)=2c ^(1/2) +2l ^(1/2) where c is the...
Suppose that the consumer’s preferences are given by U(c,l)=2c ^(1/2) +2l ^(1/2) where c is the level of consumption and l is leisure. The consumer has to allocate 50 hours between leisure and labour. The real wage rate is 10 per hour and the real non-wage income is 160. Assume that there is no government. Note that (∂c ^(1/2)) / (∂c) = (1/2) c^(-1/2) (a) Write the budget constraint of the household. (b) Solve for the tangency condition using the...
(Intertemporal Choice )Consider a consumer whose preferences over consumption today and consumption tomorrow are represented by...
(Intertemporal Choice )Consider a consumer whose preferences over consumption today and consumption tomorrow are represented by the utility function U(c1,c2)=lnc1 +?lnc2, where c1 and c2 and consumption today and tomorrow, respectively, and ? is the discounting factor. The consumer earns income y1 in the first period, and y2 in the second period. The interest rate in this economy is r, and both borrowers and savers face the same interest rate. (a) (1 point) Write down the intertemporal budget constraint of...
Santi derives utility from the hours of leisure (l) and from the amount of goods (c)...
Santi derives utility from the hours of leisure (l) and from the amount of goods (c) he consumes. In order to maximize utility, he needs to allocate the 24 hours in the day between leisure hours (l) and work hours (h). Santi has a Cobb-Douglas utility function, u(c, l) = c 2/3 l 1/3 . Assume that all hours not spent working are leisure hours, i.e, h + l = 24. The price of a good is equal to 1...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT