4. Assume Megan has preferences represented by utility function U (x₁, x2) = (x₁)¹/4 (x2)³/4 Good 1 is electricity (1) while good 2 is gasoline (x2). Suppose the consumer has an income level of m= 1000 dollars. In addition, the price of good 1 is p₁ 5 and the price of good = 2 is p2 = 5. (a) Compute the Marginal Rate of Substitution (MRS). (b) Find the optimal levels of electricity (x) and gasoline (x) consumption for Megan. (c) Suppose the government imposes a per-unit tax of t = 5 dollars on gasoline. Find the optimal levels of electricity (x) and gasoline (x) consumption for Megan with the tax.

4. Assume Megan has preferences represented by utility function U (x₁, x2) = (x₁)¹/4 (x2)³/4 Good 1 is electricity (1) while good 2 is gasoline (x2). Suppose the consumer has an income level of m= 1000 dollars. In addition, the price of good 1 is p₁ 5 and the price of good = 2 is p2 = 5. (a) Compute the Marginal Rate of Substitution (MRS). (b) Find the optimal levels of electricity (x) and gasoline (x) consumption for Megan. (c) Suppose the government imposes a per-unit tax of t = 5 dollars on gasoline. Find the optimal levels of electricity (x) and gasoline (x) consumption for Megan with the tax.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X = 30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? < (d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain.< (e) State the consumer's maximization problem and express this in words.< (f) Now let Px = 10, Px= 20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility (U*). Show your work. < (g) Now let Py = 15. How does optimal consumption (X*.Y*) and utility (U*) change relative to (e)? Explain in simple terms and show in a diagram.<
2)Ben is choosing between cookies and soda. Denote the marginal utility of cookies is MUc, and the marginal utility of soda is MUs. Which of the following relationship is true regarding the marginal utility of substitution (MŘS) of cookie in terms of soda? A) MRS= MUc B) MRS = MUS C) MRS = MUS / MUC D) MRS = MUc / MUs
Suppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25?
Suppose the preferences of an individual are represented by a quasilinear utility function: U(x, y) = In(x) + 3y a) Initially, Px=1, Py=6 and 1=102. Then, the price of x increases to 2 (Px=2). Calculate the changes in the demand for x. Please also calculate the substitution and income effects of the change in Px on x. (Hint: since the change in price is not small, you cannot use the Slutsky equation. You need to have numbers instead of functions as the answer.) B)Please also calculate the substitution and income effects of the change in Pr on y. C) Instead of doubling to 2, suppose Px is only increased by a small amount. Use the Slutsky equation to find the substitution and income effects of the change in the price of x on x. Compare your result to (a). Explain why there's no income effect of the change in Pa On X. Show your result on an indifference curve. d) Use the Slutsky equation to find the substitution and income effect of the change in Px on y. Compare your result to (b).
Sarge's utility function is U(X1,X2)= X1*X2. If his marginal rate of substitution (MRS) is 3 and he is currently consuming 36 units of good 2, how many units of good 1 is he consuming? [A] Please put your answers in numerical values with no comma or decimal places.
Joan has the following utility function: u(x, y) = 5x + 3y. Consider that income is I = $8, and prices are given as pa = $4, p = $2. (e) Assume the price of y increases to 4. Find the total, income and substitution effects for x. Consider this price change a "large" price change.
3. The utility that Elena receives by consuming food F and clothing C is given by U(F, C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is £22. MUF = C+1 and MUc = F. (i) Define the term Marginal Rate of Substitution (MRS) (ii) Find the utility maximizing values of C and F for the numerical values given above (Hint: You can assume interior solution). (iii) Now suppose that price of C and Elena's income remain unchanged at £2 per unit and £22, respectively, while the price of F varies. Find the equation of the demand for F as a function of the unit price of F (PF).
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Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5 2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).
2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂
Peter's preferences over two goods, x and y, are represented by the utility function u(x, y) = y + 2x. a) Peter is currently consuming bundle A = (2,4) with 2 units of good x and 4 units of good y. Calculate his current level of utility from consuming this bundle. b) Write the expression the indifference curve representing Peter's current level of utility (i.e., the one you found in part (a). Next draw this indifference curve. c) By looking at the indifference curve you drew in part (b), answer the following questions: Does Peter like good x? Good y? Explain. What can you say about the marginal rate of substitution of good x for y, MRSxy? Is it positive? Negative? Constant? Increasing? Decreasing? Interpret/explain your answer in terms of the tradeoffs Peter is willing to make between goods to keep the same utility level. d) On the same graph you drew in part (b), draw the indifference curve for a utility level of 10. Plot and label in the graph bundles B = (1,2), C = (1,6), and D =…