5. Assume Mark's utility function is given by u(x1, x2) = x1x2. The prices of goods 1 and 2 are p₁ and p2, respectively, and his income is m. (a) Find the optimal levels of consumption for goods 1 and 2. (b) Assume the government imposes a per unit tax t on good 1. Find his new consumption bundle. (c) Now assume the government imposes an income tax of tion bundle. tm 2(p₁+t)* Find his new consump-

5. Assume Mark's utility function is given by u(x1, x2) = x1x2. The prices of goods 1 and 2 are p₁ and p2, respectively, and his income is m. (a) Find the optimal levels of consumption for goods 1 and 2. (b) Assume the government imposes a per unit tax t on good 1. Find his new consumption bundle. (c) Now assume the government imposes an income tax of tion bundle. tm 2(p₁+t)* Find his new consump-

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 6QFR

See similar textbooks

Similar questions

1. An agent consumes quantity (X1,X2) of goods 1 and 2. Here is his utility function: U (x1,x2) = x13x2, his budget constraint is: p1x1+p2x2=m. (a) Calculate the agent's Marshallian demand (x*, x*2). (b) Derive the agent's expenditure function. (c) Roy's identity for good 1 states that: aV(pl,p2, m)/ х1* 3 дV (р1, р2, т) am Verify this equation (you need not verify it for good 2).
3. Assume that the price of goods x increases. If x is a normal good, the substitution effect alone leads to a decrease in consumption of x.
1.Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to ﬁnd that of Y) when your preferences are represented by the utility function U = x^2y. Is X normal good? Can you conﬁrm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derived. 2.Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to ﬁnd that of Y) when your preferences are represented by the utility function U = x + xy + y. Is X normal good? Can you conﬁrm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derived 3.There are two goods F and C. Let MU and P denote marginal utility and price of each good. SupposeMUF = 3, MUC = 4, PF = 2, PC = 2.Are you maximizing your satisfaction? If not, what would you do to increase your satisfaction? Explain.
3. Suppose you consume two goods, whose prices are given by p₁ and p2, and your income is m. Solve for your demand functions for the two goods, if (a) your utility function is given by U(x₁, x2) = ax₁ + bx₂ (b) your utility function is given by U(x₁, x2) = max{ax₁, bx₂}
There are two goods in an economy: apples (a) and bananas (b). Price of anapple is $1 and price of a banana is $2. Your income is $10. Suppose your utility function isu(a, b) = 2a2 b+5a. (8 points) How many apples and bananas will you consume?b. (4 points) Are a and b normal or inferior goods?c. (4 points) Are a and b substitutes or complements?d. (4 points) Draw the Engel curve for apples for the income levels ranging from $10, $20,$30 and so on.
19. If people consume less of a good when their income increases, it is call a) a subsidy b) a compliment c) a normal good d) an inferrior good
5. Suppose the utility function for goods x and y is given by U (x, y) = xY + y (i). Calculate the uncompensated (Marshallian) demand functions for x and y, and describe how the demand curves for x and y are shifted by changes in I or the price of the other good. (ii). Calculate the expenditure function for x and y. (iii). Use the expenditure function calculated in part (b) to compute the compensated demand functions for goods x and y. Describe how the compensated demand curves for x and y are shifted by changes in income or by changes in the price of the other good.
Harry consumes 2 goods, X and Y and he spends N$60 per month. The price of good X is N$4 and the price of good Y is N$10. Harry's utility function is U(X, Y) = XY. (i) What is Harry's marginal rate of substitution? (5) (ii) What is the expression for Harry's budget constraint? (3) (iii) What is the slope of Harry's budget constraint? (2) (iv)Find the values of good X and Y maximizes Harry's utility. Show all your work. (6) (v) Illustrate Harry's utility maximizing combination on a clearly labelled graph. (4) (vi) Suppose the price of good X increased to N$6. Illustrate Harry's income and substitution effects on a well labelled graph. Show your work. (10) (vii) Suppose Genie is consuming two goods, coffee and beer. She spends all her income on a combination of coffee and beer where MUcoffee/Peoffee is 5 and MUbeer/Pbeer is 3. Explain why this combination is not maximizing her satisfaction. What should she do to maximize her utility? (5)
1 Jane consumes two goods, shoes, s, and housing, h. Her income is M and the prices 57/317/3 of s and h are Ps and Ph, respectively. Jane's utility function is Us Find the following: a Marshallian demand functions b. Derive the price elasticity for housing. What is the cross price elasticity for housing? Derive the expenditure-income elasticity for housing (that is, the % change in expenditure on h when there is a 1% change in income)? What about the Cobb-Douglas demand functions explains these elasticities. C. Derive the indirect utility function and expenditure function d. Using Shephard's Lemma, derive the Hicksian demand functions e. Perform a Slutsky decomposition for housing (that is, what is the total effect on quantity demanded when there is a change in price and also what is the income and substitution effect). Now assume income is $1,500, the price of shoes is $8 and the price of housing is $125. f. What is the quantity demanded of housing? Now assume the government…
2. Think about a consumer with a utility function of U(x,y) =2xy+1, his budget constraint is px*x +py*y = m. а. Please derive the Marshallian demand functions. b. What would happen to the demand of each good if m increases(assume price positive)? Are they normal good or inferior good? Please derive the indirect utility function. Please derive the expenditure function. С. d.
consumptionA consumer's budget constraint is given by 500 = 40G + 10D, where G is ice cream in liters and D is drink in liters. The consumer thinks that a liter of ice cream is a perfect substitute for 3 liters of drink. Which statements are then correct?Select one or more options: a-2 liters of ice cream and 42 liters of drink are on the budget line b-The optimal choice is to consume 3 times as much drink as ice cream c-The optimal choice is to only consume ice cream d-0 liters of ice cream and 50 liters of drink are on the budget line
a. Determine the demand functions of x and y in the case of a Cobb-Douglas type utility function, in the following cases: α=0.40;β=0.60 Graph the demand functions of the two goods (price as a function of quantity) assuming the individual's income is $500 - Determine what is the quantity demanded of x and y, if the price of good x is USD 1, the price of good y is USD 4, and income is USD 500 - Now, explain what happens to the quantity demanded if the prices of the goods are doubles holding income constant.