6. Suppose that a fast-food junkie derives utility from three goods - softdrinks (x), 0.5 0.5 hamburgers (y), and ice cream sundaes (2) - according to the Cobb-Douglas utility function U(x, y, z)=xºsyas (1+z)05. Suppose also that the prices for these goods are given by p=0.25, p, = 1, and p. = 2 and that this consumer's income is equal to 2. a) How much will this consumer buy of each good to maximize utility? b) Show that the utility function is maximized (Use |H₂| to identify whether it is a maximum or a minimum). c) What is the maximum utility of the fast-food junkie?

6. Suppose that a fast-food junkie derives utility from three goods - softdrinks (x), 0.5 0.5 hamburgers (y), and ice cream sundaes (2) - according to the Cobb-Douglas utility function U(x, y, z)=xºsyas (1+z)05. Suppose also that the prices for these goods are given by p=0.25, p, = 1, and p. = 2 and that this consumer's income is equal to 2. a) How much will this consumer buy of each good to maximize utility? b) Show that the utility function is maximized (Use |H₂| to identify whether it is a maximum or a minimum). c) What is the maximum utility of the fast-food junkie?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

10
2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
When do we differentiate between using the formula MU(x) = TU(x) – TU(x – 1) and Marginal Utility = Change in Total Utility (ΔTU) / Change in No. of Units Consumed (ΔQ) when calculating marginal utility. This is confusing to me. On that note, which formula should we use for the below scenario? Part 1 Given the quantity of total movie tickets and total concession stand items consumed in a month and the total utility derived at Ruby Red Movie Theater for each, calculate the marginal utility and the marginal utility per dollar for movie tickets and average concession stand items. Step 1: Calculate marginal utility and marginal utility per dollar for movie tickets. Quantity of Tickets Consumed Total Utility Marginal Utility Movie Ticket Price Marginal Utility Per Dollar for Movie Tickets 0 0 --- --- --- 200 150 $10.00 400 275…
please teach solve explain step by step
Show clear and step by step solutions.
Alice is going to Wonderland and needs supplies. She has $100 and can buy only walnuts and raisins. The price of walnuts is $20 per kg and of raisins is $10 per kg. Alice's preferences are described by the utility function u(x1,x2)=min{0.5*x1+2*x2,x1}, where x1 is the quantity of walnuts, and x2 is the quantity of raisins. Given her budget constraint and preferences, if Alice were offered a choice only among the bundles listed below, which one would she buy? Выберите один ответ: a. x1=3, x2=4 b. x1=2, x2=0.5 c. x1=4, x2=3 d. x1=1, x2=8
Solve these consumer choice problems: a. Suppose a consumer has a utility function u(x, y) = xy + 7y facing prices p,=S1 and p,=$2 and income I = $10. Draw a diagram and find the consumer's optimal consumption of goods x and y. b. Suppose that you are in a situation where you can afford purchasing 3 units of good x and 4 units of good y. You discover that another affordable bundle of 5 units of good x and 2 units of good y causes you to reach the same level of utility. Assume that your utility function and budget line are both well behaved. Are you maximizing your utility by consuming your original bundle? Why or why not? Propose an alternative, affordable bundle that would yield a higher utility level than either of the original bundles.
1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?
Please get correct
2) A consumer of two goods, either 1 or 2, has a utility function U (X1, X2) = x1 0,6.x2 0.4, where x denotes units of good 1 and x2 units of good 2. The price of good 1 is 5 euros per unit, the price of good 2 is 3 euros per unit and the consumer's income is 150 euros. Suppose only the price of good 1 changes and so does the new one price is p1‘ = 2. Then the Slutsky substitution effect with respect to good 1 is Choose one: A) Not defined B) 10.8 C) 8.8 D) 7.8 E) 9.8
1. Consider a consumer who consumes two goods. The utility function is given by u(x1, x₂) /2x1+1+√√√x₂, - where x > 0 denotes the amount of good i = the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. 1,2 consumed. Unless stated otherwise, (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x₁, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its derivative with respect to p2, i.e., v'(P2), at p2 = 3. (4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand for each good.
Help!