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.
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- 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…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.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 C
- 4. Steve's utility funetion over leisure and consumption is given by u(L,Y) = min (3L, Y). Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 5. Find the optimal leisure - consumption combination. What is the amount of hours worked? (b) Suppose the overtime law is passed so that every worker needs to be paid 1.5 times their current wage for hours worked beyond the first 8 hours. Will this law induce Steve to work more hours? If so, how many? If not, explain.4. A consumer’s utility function over leisure and consumption is given by u(L, Y) =LY. Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 10. Find the optimal leisure - consumption combination. (b) Suppose the overtime wage law is passed so that the firm must pay 1.5 times the normal wage for hours worked beyond the first 8 hours. Find the effect on the hours worked. Decompose the effect into substitution effect and income effectSuppose your weekly allowance from your parents is $100 and your part-time job pays $10 per hour. The slope of the line plotting the relationship between the hours worked per week (the horizontal axis) and the income per week (the vertical axis) is $. (Enter your response as an integer.) Suppose you start with 10 hours of part-time work and then decide to increase your time working by 3 hour(s). By how much will your weekly income increase? $. (Enter your response as an integer.) Suppose you start with 10 hours of work and then decide you need additional income of $20 per week. How many additional hours would you have to work? hours. (Enter your response as an integer.)
- 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?3. John's utility function is U(C, L) = C1/2L!/2. The most leisure time he can consume is 110 hours. His wage rate is $10. Find John's optimal amount of consumption and hours for leisure and work.Damon's wage rises. The substitution effect would cause him to his work hours, and the income effect would cause him to his work hours. decrease; increase O increase; increase increase; decrease O decrease; decrease
- Problem Set 1. A firm's production function is º=50L-0.01Ľ' , where L denotes the size of the workforce. Find the value of MP in the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form A P = Q" where A and n are positive constants. 3. The demand and total cost functions of a good are respectively 4P+Q-16=0 and ТС %3D 4 + 20 — 10 20 a) Find expressions for TR, (profit) 1 , MR, and MC in terms of Q. b) Solve the equation dn = 0 ÕP and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢'/, million per floor (e) Specialized costs of GH¢10000× per floor. How many floors should the office complex contain if…1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y)=LY+2L a. b. C. Calculate the demand function for L and show it on a graph (L vs W). Calculate the labor supply (H) and show it on a graph (H vs W). What will happen to L, Y and H if the wage per hour (W) will decrease? =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?