Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 16, Problem 16.2P
a)
To determine
To find:
Expenditure function for the given function:
b)
To determine
To know:
Compensated demand function for consumption and leisure.
c)
To determine
To ascertain:
Compensated labor supply function
d)
To determine
To Know:
Comparison of compensated supply functions.
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If the consumer's non-labor income increases while wages remain unchanged, what will
happen to the budget line?
A) The budget line shifts inward without a change in slope.
B) The budget line rotates inward from the intercept on the horizontal axis.
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D) The budget line shifts outward without a change in slope.
An optimum labor-leisure that occurs as a corner solution
A) can be an equilibrium in the aggregate economy.
B) includes the consumption of only one good.
C) cannot exhaust the budget constraint.
D) includes the exact same amounts of each good.
) If a firm is a price taker in both the labor market and the output market, it will
A) hire labor until the marginal product of labor equals the output price.
B) hire labor until the marginal product of labor equals zero.
C) earn zero economic profit in the short run.
D) hire labor until the marginal product of labor equals the wage rate.
Consider a consumer who could earn $400 per week and has 50 weeks available each year to allocate between work (H) and nonmarket time (L). They have no non-labour income. Their utility function is U = C2L , where C is the value of consumption goods. What is their optimal choice for the number of weeks in nonmarket time and consumption? Show this in a diagram.
Suppose the government introduces a policy that (i) offers no benefits to people who do not work, (ii) offers a wage subsidy on earnings at a rate of 25%, with a maximum benefit of $5000, and (iii) the benefit is subject to reduction at a rate of 25% for every dollar earned above $20,000 in the year. Show the person’s new budget constraint in a new diagram, and discuss how the person’s optimal choice might change (you do not have to calculate this, but point to where it is likely on the new budget constraint). Discuss how income and substitution effects play a role.
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- On average, people sleep 8 hours per day meaning that each individual has 16 hours per day to allocate between labour and leisure. Assuming that the wage rate is $15 per hour and there are non-labor income is zero. The utility function of an individual is given by U(Y, L) = YL and for simplicity, the price index for real income is 1. a. Determine the budget constraint. b. Determine the marginal rate of substitution. c. What are the optimal labor and leisure hours? d. At the optimal relationship, what is the utility level for the individual?arrow_forwardAssume Lorena derives utility from consumption and leisure. Through the following utility function. U=VC-R where C is consumption and R is hours of leisure consumed per day (there are 24 hours in her day). Let w be the wage rate and H be the hours of work chosen. The price of consumption goods, C, is $1. In addition, assume Lorena has $M amount of non- wage income each day. Set up the utility maximizing Lagrangian needed to maximize utility subject to the budget constraint but do not solve for the demand for C and R. a b. Draw the consumer choice model for this situation (fully label the graph). Use it to graphically derive/describe/explain her labor supply function and explain what would be true for her labor supply to rise or fall when the wage rises (you may want to draw the graph twice. Measure and explain the loss in consumer surplus using the concept of compensating variation. g. h. What is the expenditure-price elasticity equation for y? That is, the elasticity for the % change…arrow_forwardWinona has 80 hours to divide between leisure and labor. Her utility function is u(r,c) = f(r) + c, when r represents hours of leisure,c represents dollars of consumption, and f is strictly concave. Winona’s wage is w0= $15/hr. initially, then it rises to w1= $20/hr. (i) Explain what happens to Winona’s labor supply when the wage rises,and why. (ii) Explain how the answer to (i) would change if Winona were to win a lottery.arrow_forward
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- Determine whether the following statements are true, false, or uncertain. Please illustrate and explain your answer. If leisure is a normal good, then an individual's labor supply curve must be positively sloped. If leisure is an inferior good, then an individual's labor supply curve must be negatively sloped.arrow_forwardSharon spends her time (16h) between leisure (L) and work and he consume Y product from his working income (P=1). Assume that she gets W$ per hour of working (W>0) and has the following utility function: U (L, Y) =LY 4Y. a.Calculate the demand function for L. and show it on a graph (L. vs W). b. Calculate the labor supply (H) and show it on a graph (H vs W). c.What will happen to L. Y and H if the wage per hour (W) will decrease?arrow_forwardQuestion 2 - Consider a consumer with utility function U = x1 + x2 12, where is the labor supplied, x₁ and x2 are the quantity of consumption for good 1 and 2 respectively. The price of good 1 and 2 are p₁ and p2 respectively (P1, P2 > 0). The consumer cannot spend more than its earning from working, and has no other source of income. The consumer has an hourly wage rate of w. In the short-run, the consumer has signed a work contract that the work hour is fixed at ī> 0. The consumer cannot consumer negative amount of quantity of goods. a) Write down the constraints faced by the consumer in the short run. b) Find the utility maximising quantity of consumption for good 1 and 2 in the short run. Assume p₁ > P₂• c) In the long run, the consumer could choose the labour supply 1, i.e. I is not fixed and is a choice for the consumer. The consumer cannot work more than 24 hours a day, and cannot work negative amount of hours. Find the utility maximising quantity of consumption and labour…arrow_forward
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