Suppose a worker's utility function is U(C, L) = C^2 +(2nL)^2 , where C denotes consumption...

Suppose a worker's utility function is U(C, L) = C^2 +(2nL)^2 , where C denotes consumption and L leisure. Let T denote time available to split between leisure and work, w denote the wage rate and V = 0 denote non-labor income (as in the lecture).

(a) What is the worker's optimal choice of C and L as a function of w, T, and n?

(b) What is the worker's reservation wage as a function of T and n?

(c) Suppose the labor market consists of a hundred workers with the above utility function, but the value of n is different for all of them. In particular, there is precisely one worker with n = 1, precisely one with n = 2, etc. Describe how you would construct the aggregate labor supply curve, i.e. the number of workers who would be willing to supply labor at any given w.

(d) What employment level corresponds to w = 13?

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Jo has preferences described by the utility function, U = c0.5r0.5. Where c denotes her consumption...

Jo has preferences described by the utility function, U = c0.5r0.5. Where c denotes her consumption of carrots in ounces and r denotes her consumption of red meat in ounces. She faces two constraints, 1) she has an income of 1000 and the price of c is 10, while the price of r is 20. 2) due to health concerns, the government does not allow anybody to consume more than 80 ounces of r. a) write down the Lagrangian and...

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.

Amy’s utility function is U = √ C, where C is consumption and is given by...

Amy’s utility function is U = √ C, where C is consumption and is given by C = Income − Expenses. Amy’s income is $10,000 and there is a 5% chance that she will get sick, which would cost $3,600 in medical expenses. (a) (5 points) What is Amy’s expected utility if she doesn’t have insurance? (b) (5 points) What is the actuarially fair premium for a full-coverage insurance plan? What is the actuarially fair premium for an insurance plan...

Consider an economy where the representative consumer has a utility function u (C; L) over consumption...

Consider an economy where the representative consumer has a utility function u (C; L) over consumption C and leisure L. Assume preferences satisfy the standard properties we saw in class. The consumer has an endowment of H units of time that they allocate to leisure or labor. The consumer also receives dividends, D, from the representative Örm. The representative consumer provides labor, Ns, at wage rate w, and receives dividends D, from the representative Örm. The representative Örm has a...

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....

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...

A person's utility function is U = C1/2 . C is the amount of consumption they...

A person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year. a. What is their expected utility? b. Calculate the actuarially fair insurance premium. c. What would their expected utility be if they purchased the actuarially fair insurance premium?

The consumer’s utility function is U(a,b) = ab2, where a denotes the quantity of good A...

The consumer’s utility function is U(a,b) = ab2, where a denotes the quantity of good A that the consumer consumes and b denotes the quantity of good B that the consumer consumes. The price per unit of good A is 4 Euros and the price per unit of good B is 8 Euros. Consumer’s income is 120 Euros. a) Find the marginal utility of good A and the marginal utility of good B b) Find the optimal quantity of good...

Consider an individual with the following utility function: U = min{c, h} Where c is consumption...

Consider an individual with the following utility function: U = min{c, h} Where c is consumption and h is leisure. The wage rate is $15 per hour, and the total number of hours available to the individual is normalized to 1. Find out the optimal level of consumption, leisure and labor. The government imposes a tax of $2 per hour of labor. Find out the new optimal values of consumption, leisure and labor. Comment on the form of the utility...

Subjects