1. An individual derives utility from the consumption of a basket of goods, c and leisure time, & given by U(c₂l) = cºl(¹-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L + l = 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given.
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- Garfield enjoys pizzas and hanging out (leisure). He sleeps 8 hours per day. Of the remaining16 hours, for each hour he chooses to work he gets paid 2 pizzas. Garfield must pay 6 pizzas intaxes but receives dividends equivalent to 6 pizzas.1. Draw Garfield’s budget constraint (put consumption on the vertical axis and leisure of thehorizontal). Make sure to show the vertical and horizontal intercepts as well as the slope.b. Now suppose that Garfield chooses to work 10 hours per day. Find how many hoursof leisure and how many pizzas he will consume.c. Using your answer from b, show Garfield’s optimal point on the budget line and drawthe indifference curve passing from that point.4. Suppose that Garfield’s wage falls to 1 pizza per hour. Draw Garfield’s new budgetconstraint. Make sure to show the value of any intercept that has changed.5. Suppose that in response, Garfield decides to work for 6 hours per day. How much leisurewill he take, and how much pizza will he consume?6. Use an…Amadea spends all her income on pizza,chocolate milk, and music streams. The price of pizza is $4 per slice and price ofchocolate milk $2 per bottle. At Amadea's current consumption level, her marginalutility for pizza is 50 units per slice and for music 100 units per stream. Assuming thatAmadea is a utility maximizer, how much is (a)her current marginal utility for a bottleof chocolate milk, and (b) the price of streams she buys. Show your work. [Hint: Ch 6:Utility-maximizing formula)25 Columns 1 through 4 in the following table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respectively, $9, $3, $2, and $6 and that Ricardo has an income of $71. Column 1 Column 2 Column 3 Column 4 Column 5 Units of Good A Units of Units of Units of MU MU MU MU Good B Good C Good D Number of Dollars Saved MU 1 72 1 24 1 15 1 36 1 5 2 54 2 15 2 12 2 30 2 4 3 45 3 12 3 8 3 24 3 3 4 36 4 9 4 7 4 18 4 2 5 27 5 7 5 5 5 13 5 1 6 18 6 5 6 4 6 7 6 0.50 7 15 7 2 7 3.5 7 4 7 0.25 8 12 8 1 8 3 8 2 8 0.13 Instructions: Enter your answers as a whole number. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? 4 units of A 3 units of B units of C units of D b. How many dollars will Ricardo choose to save?
- 3. [30+10] A consumer who consumes two goods and has the following utility function: U(x₁, x₂) = log(x₁ + 1) + log(x2 + 1), where ₁ and ₂ denote the monthly consumption of two goods. The consumer maximizes her utility subject to the following constraints: P₁x1 + P₂x2 ≤m, x₁ ≥ 0, X₂ ≥ 0, where p₁ > 0, p2 > 0 and m > 0. [Hint: Note that log f(x) = f(df (2).] 1_df f(x) dx (a) Write down the Kuhn-Tucker conditions for a point (x₁, x2) to solve the problem, and find all points that satisfy the conditions. Do any of those points solve the problem? (b) Show the above results by drawing indifference curves and budget set on the x₁x2 plane.5. Suppose the representative consumer has the (quasilinear) utility function: U(x, y) = ax + In(v) where x,y are consumption goods. Denominated in US dollars, the prices of x and y Pi and pz, respectively. (a) What does the term quasilinear mean? Is consumption of x independent of y? (b) Assume the consumer has a budget of C dollars at his/her disposal. What is the maximum utility the consumer may achieve with this budget? (c) What is the minimum expenditure if the consumer wants to derive U,units of utility?Garfield enjoys pizzas and hanging out (leisure). He sleeps 8 hours per day. Of the remaining16 hours, for each hour he chooses to work he gets paid 2 pizzas. Garfield must pay 6 pizzas intaxes but receives dividends equivalent to 6 pizzas.1. Draw Garfield’s budget constraint (put consumption on the vertical axis and leisure of thehorizontal). Make sure to show the vertical and horizontal intercepts as well as the slope.b. Now suppose that Garfield chooses to work 10 hours per day. Find how many hoursof leisure and how many pizzas he will consume.c. Using your answer from b, show Garfield’s optimal point on the budget line and drawthe indifference curve passing from that point.4. Suppose that Garfield’s wage falls to 1 pizza per hour. Draw Garfield’s new budgetconstraint. Make sure to show the value of any intercept that has changed.5. Suppose that in response, Garfield decides to work for 6 hours per day. How much leisurewill he take, and how much pizza will he consume?6. Use an…
- 2nd attempt See Hint A consumer faces a tradeoff between labor (L) and leisure (R). She consumes a composite good (C). When the consumer works, she earns an hourly wage of $15.00, and she spends a maximum of 24 hours on labor and leisure, but she chooses to work 10.00 hours. Whatever time she does not spend working, she spends on leisure. She starts with an initial endowment of 11.00 units of the composite good, which she can buy and sell freely at a market price of $4.00. Given this information, what is the consumer's real wage? $ 1941.In income substitution effects acts in opposite direction, then the total effect on consumption is always negative. (T/F)The graph given below indicates Marshall's marginal utility for two products, A and B. Marginal utility 24 20 16 12 8 4 0 (1) Quantity 1 2 3 4 5 6 2 (2) Product A MU 4 Quantity of A: Quantity of B: 6 8 Quantity per period (3) Product A (4) MU per $ Product B (at $2) MU 10 Product A Product B 12 a) From the graph above, complete columns 2 and 4 of the table above. Round your answers to whole numbers. b) If the price of both products is $1, what quantity of each good would Marshall purchase if his budget was $8? Quantity of A: Quantity of B: c) Suppose that the price of product A increases to $2. Complete column 3 of table above. d) If Marshall's budget remained the same, what quantities of each good would he now purchase?
- John works in a shoe factory. He can work as many hours per day as he wishes at a wage rate w. Let C be the amount of dollars he spends on consumer goods and R. be the number of hours of leisure that he chooses. John's preferences are represented by U(C, R) = CR utility function Question 2 Part a John earns $8 an hour and has 18 hours per day to devote to labor or leisure, and he has $16 of nonlabor income per day. Draw John's indifference curves, budget constraints and solve for his optimal consumption and leisure choices.3. Based on each scenario in this question, indicate whether the following statements is true or false, and briefly explain your reasoning. You may also want to use a graph in your explanation if you think it's necessary. a) Mike makes $500 per week and spends all her income on books and tea. Books cost $25 each, and Mike buys 16 each week. Tea costs $5 per cup, and Mike buys 20 cups. When Mike's income falls to $450 per week, he cuts his consumption of books by 3 books and purchases 5 more cups of tea. Based on Mike's consumption behaviors, books are an inferior good and Tea is a normal good. b) Lucy consumes food and clothing. For incomes near her current income, her income expansion path is negatively sloped. Assume that food is measured along the horizontal axis and clothing is measured along the vertical axis. Therefore, at current income levels, both food and clothing must be inferior good. c) For any normal goods, the income and substitution effects work in the same direction.…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 ?