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- cook -int ences a) Chika has calculated the marginal utility that she derives from her paid employment and from leisure. This is presented in table below. In her ideal world, where she could work as few or as many hours as she wished, how would she allocate her sixteen waking hours? (She does need to sleep.) Hours 1 2 3 4 5 6 7 8 9 10 MU Paid Employment 80 75 70 65 60 55 50 45 40 35 MU Leisure 120 110 100 90 80 70 60 50 40 30 9 hours working and 40 hours leisure. b) Unfortunately, Chika begins to realize that unless she gets an education she will not enjoy a high salary and therefore, will not be able to afford more leisure time. She therefore decides to spend six hours each day studying (in addition to her eight hours of sleep). How will she now divide the remaining hours between work and leisure?! hours working and hours leisure. Help Save CProblem Set 1. A firm's production function is º=50L-0.01Ľ' , where L denotes the size of the workforce. Find the value of MP in the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form A P = Q" where A and n are positive constants. 3. The demand and total cost functions of a good are respectively 4P+Q-16=0 and ТС %3D 4 + 20 — 10 20 a) Find expressions for TR, (profit) 1 , MR, and MC in terms of Q. b) Solve the equation dn = 0 ÕP and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢'/, million per floor (e) Specialized costs of GH¢10000× per floor. How many floors should the office complex contain if…Assume that a person earns $10 per hour and her non-labor income increases from $100 to$200. She also has 110 hours a week to decide either to work or leisure. a. Draw a budget constraint of this person.b. Draw an indifference curve to show the income and substitution effect of change innon-labor income. HINT: you can draw two separate graphs to show the effect ofsubstitution and income effects.
- Income $240 $192 0 15 16 17 a) Using the above diagram, decompose the effect of a wage decrease for this individual into Income Effect (IE) and Substitution Effect (SE). Leisure 24 b) How many hours of work is effected because of the IE? c) How many hours of work is effected because of the SE? d) What is the net effect of this wage decrease on hours of work for this individual?A worker earns £15 pounds an hour and chooses to work six hours a day. The worker has noother source of income. For the question below, assume that the worker has “standard” Cobb-Douglas preferences. When considering wage changes, assume that the “income effect”outweighs the “substitution effect”. (a) Write down the worker’s budget constraint and then represent the worker’schoice in a suitably labelled graph. (b) The government gives the worker £80, but taxes the worker’s wage, such thattheir take-home wage is £10. Model this policy in a suitably labelled graph. Isthe worker better off (in terms of utility) after this policy? Note –there are arange of correct answers for the worker’s new hours/income. Choose one thatis consistent with the information given in the question.7. An individual's utility function is given by U =1000x, +450x, +5 x,x, -2x - x where x, is the amount of leisure measured in hours per week and x, is income earned measured in cedis per week. Determine the value of the marginal utilities, when x, = 138 and x, = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?
- b. i. Explain the concept of Marginal Rate of Substitution (MRS) as an important tool of indifference curve analysis of demandNo written by hand solution and image There have been suggestions that the "work ethic" in the U.S. has declined. The claim is that, as a result, people are choosing to work fewer hours (at a given wage rate and level of unearned income) than did individuals in the past. This can be indicated by changes in individuals' indifference curves. Show such a change in indifference curves on graph with the consumption good on the Y-axis and leisure on the X-axis. How does the slope of the indifference curve change at a given level of leisure? (It may be useful to draw a simple budget constraint to indicate the change in hours of work.) Show such a change in indifference curves on graph with the consumption good on the Y-axis and leisure on the X-axis. How does the slope of the indifference curve change at a given level of leisure? (It may be useful to draw a simple budget constraint to indicate the change in hours of work.)a) Chika has calculated the marginal utility that she derives from her paid employment and from leisure. This is presented in table below. In her ideal world, where she could work as few or as many hours as she wished, how would she allocate her sixteen waking hours? (She does need to sleep.) Hours 1 2 3 4 5 6 7 8 9 10 MU Paid Employment 105 95 85 75 65 55 45 35 25 15 MU Leisure 100 90 80 70 60 50 40 30 20 10 hours working and b) Unfortunately, Chika begins to realize that unless she gets an education she will not enjoy a high salary and therefore, will not be able to afford more leisure time. She therefore decides to spend six hours each day studying (in addition to her eight hours of sleep). How will she now divide the remaining hours between work and leisure? hours working and hours leisure. hours leisure.
- 5. Cindy gains utility from consumption C and Leisure L. Then most leisure she can consume in any given week is 110 hours. Her utility function is U (C, L) = C × L. Cindy receives $660 each week from her great-grandmother. (a) Find her marginal rate of substitution |M RS|. (b) Find her reservation wage. (c) Interpret the reservation wage.Suppose that a person has 2000 hours to allocate each year between leisure and work. a. Derive the equation of his budget constraint given an hourly wage of $(15)/hour. b) Graph his budget constraint line based on the equation you derived in part a. (Consumption (C) on the vertical axis and leisure (L) on the horizontal axis). Please make sure to include the value for the vertical and horizontal intercepts. c) Now suppose that the local government introduces an income guarantee program for single parents in which the income transfer is $10,000 per year if an individual does not work during that year (this dollar amount represents the benefit guarantee). If the individual decides to work, this transfer program imposes a 100% benefit reduction rate (e. g.. each additional hourly wage earned is reduced by 100%). Derive the new budget constraint equation that corresponds to this scenario. d) Draw the budget line that corresponds to the new scenario on a new graph. (Consumption (C) on the…For this question, assume that indifference curves are strictly convex, consumption andleisure are normal goods, and the optimal amounts of consumption, leisure, and labor arealways positive. A wage increase ______. (SE = substitution effect; IE = income effect)(a) increases labor supply via the SE and decreases labor supply via the IE(b) decreases labor supply via the SE and decreases labor supply via the IE(c) increases labor supply via the SE and increases labor supply via the IE(d) decreases labor supply via the SE and increases labor supply via the IE(e) Can’t tell without knowing the utility function
