Consider the figure to the right, where a consumer initially maximizes utility at consumption-leisure combination R along budget constraint L¹. Suppose the wage rate doubles. 1.) Use the line drawing tool to draw the new budget constraint with the higher wage. Label this line 2. 2.) Use the point drawing tool to plot the new utility-maximizing combination of consumption and leisure. Label this point 'T'. Carefully follow the instructions above, and only draw the required objects. As the wage increases, the hours worked by the individual In this case, leisure is good. Income (Market value of goods) per day 240 220- 200 180 160 140 120- 100- 80- 60 40 20- L¹ 2 4 R 43344 6 8 10 12 14 16 18 20 22 24 26 Leisure hours per day O O R
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- 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…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…. An individual's utility function is given by u = 1000 x, + 450 x. + 5x, 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. Det er mine the value of the marginal utilities, when x, = 138 and x= 500. Hence est imate the change in utility if the individual works for an extra hour, which increa ses earned income by GH¢ 15 per week. Does the law of diminishing ut ility hold for this function? %3D
- 3. Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 5A/4B³/4. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method. b. Suppose Pa increase. Show graphically the income, substitution effect and total effect and explain. c. Suppose PA increase. Show the graph for CV and EV and explain.Suppose a consumer has a monthly income of m = 100 which she spendson two commodities: french fries (x1) and beef jerky (x2). The price offrench fries is p1 = 2 and the price of beef jerky is p2 = 5. (e) What is the slope of the budget line? Provide an economicinterpretation of this number.(f) Because of Mad Cow Disease, the price of beef jerky increasesto $10 (lower supply of beef). On a new graph, plot the originaland new budget constraint clearly identifying how the budgetconstraint has changed. What is the new relative price of beefjerky in terms of french fries?(g) Because of severe shortages, Congress passes the Jerky ReliefAct which limits each consumer to purchase at most 5 packs ofjerky. Show on a graph how this affects the consumer’s budgetset. Answer all three.Pls help with thsi question Consider an Individual who buys films (F) and books (B) with the following utility function:?(?, ?) = 5? + 2?This individual also has the following incomes (m) and prices (pF and pB):? = $50, ?f= $5, ?b= $10Given the above:1) Draw the utility functions for utility levels of 10 and 20. Draw these with films on the x-axis and books on the y-axis. 2) What is the MRS for these utility functions? Assume that films remain on the x-axis andbooks remain on the y-axis. 3) What is the consumption bundle that delivers the highest level of utility that is alsoaffordable?
- An individual’s utility function is given by where is the amount of leisure measured in hours per week and is income earned measured in cedis per week. Determine the value of the marginal utilities, when = 138 and = 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?Draw the indifference curve for someone decidinghow to allocate time between work and leisure.Suppose the wage increases. Is it possible that theperson’s consumption would fall? Is this plausible?Discuss. (Hint: Think about income and substitutioneffects.)My Moodle My Favou tion 6 An individuals utility function is given by ret rered U = 340x1 + 960x2 + 2x1x2 – 2a- a/2, ed out of when the weekly amount of leisure is x1 132 and earned income is 12 = 760 answer the following: 1. The marginal utility of x1 is ag tion 2. The marginal utility of x2 is 3. Use the small increments formula to estimate the change in the utility when r1 decreases by 1 and x2 increases by 4. The change = 4. Does the law of diminishing marginal utility hold? 5. The MRCS at a given values is Enter non-integer numerical values as decimals to at least 3 decimal places. Note: you must use a. and not , for a decimal point. Next page revious page Mock paper ► - Working from video in SVG Jump to... format
- b. i. Explain the concept of Marginal Rate of Substitution (MRS) as an important tool of indifference curve analysis of demandGraph and explain indifference curves for the following situations:(i) An individual has constant marginal utility toconsumption in both periods.(ii) An individual does not derive utility from this period’sconsumption, but does from the next period’sconsumption.(iii) An individual’s utility decreases with consumption inboth periods.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.