Question

In: Economics

Dudley has a utility function U(C, R) = CR, where R is leisure and C is...

Dudley has a utility function U(C, R) = CR, where R is leisure and C is consumption per day.

He has 16 hours per day to divide between work and leisure. Dudley has a non-labor income of $48 per day.

(a) If Dudley is paid a wage of $6 per hour, how many hours of leisure will he choose per day?

(b) As a result of a promotion, Dudley is now paid $ 8 per hour. How will his leisure time change?

(c) Analyze the changes in Dudley’s leisure time using the substitution effect and the income effect.

Solutions

Expert Solution

(a)

U(C,R) = CR

Dudley can work for 16 hours in a day, in that case, he will earn $48 + $6(16) = $170, or he can leisure the whole day, in which case he consumes only $48.

Dudley's budget constraint is

C = 48 + 6(16 - R)

When utility function U(C,R) = C*R, the marginal rate of substitution is C / R.

Therefore, Luke's marginal rate of substitution is:

MRS = C / R.

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

w = MRS

Putting the budget constrain equation in place of C

Dudley will choose 12 hours of leisure.

His consumption will be C = 48 + 6(16 - 12) = 48 + 24 = 72

(b)

When Dudley is paid $ 8 per hour.

budget constraint is

C = 48 + 8(16 - R)

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

w = MRS

Putting the budget constrain equation in place of C

Dudley will choose 11 hours of leisure.

His consumption will be C = 48 + 6(16 - 11) = 48 + 30 = 78

(c)

The higher wage increases the price of leisure. The substitution effect of a higher wage causes the consumer to substitute labor for leisure. Higher wage induces the individual to supply a greater quantity of labor.

But the higher wage also has an income effect. An increased wage means a higher income, and since leisure is a normal good, the quantity of leisure demanded will go up. And that means a reduction in the quantity of labor supplied.

The income effect of the wage change is negative; Substitution effect of wage change is positive.

As Dudley's leisure time decreases with an increase in his wage, the strength of the substitution effect of wage change is greater than the strength of income effect.


Related Solutions

Dudley has a utility function U(C, R) = CR, where R is leisure and C is...
Dudley has a utility function U(C, R) = CR, where R is leisure and C is consumption per day. He has 16 hours per day to divide between work and leisure. Dudley has a non-labor income of $48 per day. (a) If Dudley is paid a wage of $6 per hour, how many hours of leisure will he choose per day? (b) As a result of a promotion, Dudley is now paid $ 8 per hour. How will his leisure...
Robinson has a utility of u(c, r) = cr where c = coconuts and r =...
Robinson has a utility of u(c, r) = cr where c = coconuts and r = leisure. In order to produce coconuts, technology dictates the production, given by c = a(L^1/2) where a = 8, and L = labour. The time constraint is r+L = 12. How many units of labour will be used?
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...
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,...
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...
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...
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...
Woodstock has preferences for leisure time and birdseed defined by the utility function U(l,B)= l.75B.75, where...
Woodstock has preferences for leisure time and birdseed defined by the utility function U(l,B)= l.75B.75, where l is hours of leisure time and B is the number of birdseeds Woodstock consumes. Suppose Woodstock has 24 hours a day for leisure time and for gathering birdseed. He gathers 20 birdseeds each hour he works (e.g., 20 birdseed is Woodstock’s wage). Let H be the hours Woodstock gathers birdseed. Woodstock chooses leisure time and birdseed according to the optimization problem maxl,b l.75B.75...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT