Now, suppose that Amy is laid off, but she is eligible to collect unemployment benefits of $200 per week. Use the black point (cross symbol) to represent Amy's unemployment point on the previous graph when she consumes $200 per week and has 100 hours of leisure. Suppose that after a month of being unemployed, Amy's friend Van suggests that she apply for a job at his company, where she could earn her previous salary again by working 45 hours per week.
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- 2. Utility maximization - Trading off labor and leisure The indifference curves on the following graph show Amy's preferences for leisure and consumption for increasing levels of utility, such that her utility increases in both consumption and leisure. Assuming that Amy spends 68 hours each week sleeping, she has a maximum of 100 hours available to her for leisure if she does not work at all. Initially, she works 45 hours (and thus has 55 hours of leisure) and earns $250 per week. Use the grey point (star symbol) to indicate Amy's initial leisure/consumption bundle. Dashed drop lines will automatically extend to both axes. CONSUMPTION (Dollars per week) 1000 900 800 700 600 500 400 300 200 100 0 0 + 10 20 30 40 50 60 70 80 LEISURE (Hours per week) 90 U3 100 110 Initial bundle + $200 Unemployment Benefits Equivalent Bundle, $100 Unemployment Benefits Equivalent Bundle ?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 CSuppose you expect to earn $10 this year and $10 next year. Each dollar you earn this year can be either spent, or saved at an interest rate of 10%. If you want to spend more than $10 this year, you can borrow money at 10% interest and repay it next year. Next year, you plan to pay oyour debts (if any), then spend all your earnings and all your savings (if any). Draw your budget line between “dollars spent this year" and “dollars spent next year". Suppose the government imposes a 50% income tax on all your earnings this year and next year (not including your interest earnings). Draw your new budget line. Suppose the government imposes a 50% sales tax on everything you buy this year and next year. Draw your new budget line. Suppose the government imposes a 50% income tax on all your earnings this year and next year, including your interest earnings. Draw your new budget line. True or False: If interest earnings are not subject to income tax, then an income tax and a sales tax…
- 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…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?5. Rhoda’s preferences for consumption and leisure can be expressed as U(C, L) = (C - 100) × (L - 40). There are 110 (non-sleeping) hours in the week available to split between work and leisure. Rhoda earns 10 GHS per hour after taxes. She also receives 320 GHS worth of support from her parents each week regardless of how much she works.a. What will be Rhoda’s marginal utility of leisure and her marginal utility of consumption?b. What is Rhoda’s marginal rate of substitution when L = 100 and she is on her budget line?c. Find Rhoda’s optimal amount of consumption
- 2. Utility maximization - Trading off labor and leisure The indifference curves on the following graph show Simone’s preferences for leisure and consumption for increasing levels of utility, such that her utility increases in both consumption and leisure. Assuming that Simone spends 68 hours each week sleeping, she has a maximum of 100 hours available to her for leisure if she does not work at all. Initially, she works 50 hours (and thus has 50 hours of leisure) and earns $400 per week. Use the grey point (star symbol) to indicate Simone’s initial leisure/consumption bundle. Dashed drop lines will automatically extend to both axes. [Please see the image attached] Now, suppose that Simone is laid off, but she is eligible to collect unemployment benefits of $350 per week. Use the black point (cross symbol) to represent Simone’s unemployment point on the previous graph when she consumes $350 per week and has 100 hours of leisure. Suppose that after a month of…Assume that Sara has $800 per month to divide between playing golf and playing paint ball . Assume Golf costs $40 and paintball costs $80 . Suppose Sara plays golf eight times per month and plays paintball six times per month . a. Draw Sara’s budget constraintb. Assume Sara has new expenses and can spend $320 only this month. Draw the new budget constraintc. As a result of a decrease in income Sara decides to play 11 rounds of golf and two games of paintball . what kind of a good is paintball ? what kind of a good is golf?d. Assume Sara has $400, the price of paintball is still $40 , but the price of Golf doubles , draw the new budget constraint5. Rhoda’s preferences for consumption and leisure can be expressed as U(C, L) = (C - 100) × (L - 40). There are 110 (non-sleeping) hours in the week available to split between work and leisure. Rhoda earns 10 GHS per hour after taxes. She also receives 320 GHS worth of support from her parents each week regardless of how much she works.a. What will be Rhoda’s marginal utility of leisure and her marginal utility of consumption?b. What is Rhoda’s marginal rate of substitution when L = 100 and she is on her budget line? c. Find Rhoda’s optimal amount of consumption.
- 1. How many hours will a person allocate to leisure activities if her indifference curves between consumption and leisure activities are concave (NOT convex) to the origin? 2. Tom earns $15 per hour for up to 40 hours of work each week. He is paid $30 per hour for every hour in excess of 40. Tom faces a 20 percent tax rate and pays $4 per hour in child care expenses for each hour he works. Tom receives $80 in child support payments each week. There are 110 (non-sleeping) hours in the week. Graph Tom's weekly budget line. 3. John's utility function is U(C, L) = C²/² L?/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. 4. Suppose the wage rate increased (e.g. from $10 to $20), how many hours would a worker take for work and leisure activities? Assume that the income effect dominates the substitution effect, draw a graph and explain in detail. 5. Cindy gains utility from consumption C and…1. What will be her total utility from both leisure and income when working 25 hours per week? 2. Does it make sense from the perspective of utility for Terry to increase her work hours? (Think about the total utility calculations.). Why or Why not?1. What will be her total utility from both leisure and income when working 10 hours per week? 2. Does it make sense from the perspective of utility for Terry to decrease her work hours? (Think about the total utility calculations.). Why or Why not?