1. For what kind of preferences will the consumer be just as well off facing a quantity tax as an income tax? 2. Someone is willing to maximize his/her utility. Assume he/she knows his/her u(x,y) %3D x0.Sy0.s (Cobb-Douglas) (a) Find his/her optimal consumption given the income = 20, Px=2, Py=4! %3D (b) Depict his/her optimal consumption graph! 3. Suppose that x and y (from your answer in number 2) are now perfect complement with u(x,y) = min(x,y). (a) Find his/her optimal consumption (given the same income and prices)! (b) Depict his/her optimal consumption graph!
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- Tom's income is 32. He consumes a single consumption good, C, which has a price of 2. His utility function depends on his marital status: when happily married, his utility is given byU=C^(1/2) When he is not married, his utility is given by U=0.5C^(1/2) a. Suppose that Tom is not currently married. What is his utility? Now suppose that Tom gets married.What is his utility? Assume Tom can spend all his income on his own consumption when he is married. b. Use compensating variation (CV) and equivalent variation (EV) to calculate the value of marriage to Tom. How do the two figures compare?Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…Assume the following behavioral equations for a macroeconomy: C = 100 + .9Yd, l = 50, T= $100 and G = $40 from the above behavioral equation tax multiplier is Select one: O a. 1 b. none of the options O c. 10 O d. 9
- An individual's utility function is given by: U (q1 , q2) = q11/2 . q2 Suppose we know that the individual is maximizing their utility by consuming 9 units of good #1 (q1=9) and six units of good #2 (q2=6). If the current price for good #1 is $1 (p1=1), what must be the price of good #2 (p2) and what must be the individual's current income (y) available to spend on the two goods? a.) p2 = b.) y=A consumer has utility u(x,y,z)= ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pZ = 1 . Optimally sheconsumes 30 units of z. What is her income? How much money does she spend on x?(HINT: MUX =??, MUY =??, MUZ =??and remember the “equivalent bang for the buck” condition)(b) Forget about (a). Suppose you have t = 29 hours in total to spend on 3 projects X, Y and Z to make some money.If you spend x hours on project X, you make 2√? dollars;If you spend y hours on project Y, you make ?√? dollars;If you spend z hours on project Z, you make ?√? dollars;Writing down your “utility function” u(x,y,z) and the constraint, solve the utility maximization problem; what isthe optimal amount of time to spend on x ? on y? on z ?Q18 please help fast all info is there! Suppose the utility function of U(x4, x2) = x1/2x212 and the budget constraint of p1x1+P2x2=m From 3.(2), let's assume that the consumer additionally needs to pay $20 income tax: p1=$2, p2=$2, and m=$100. Find the new optimal bundle.
- 1. Someone is willing to maximize his/her utility. Assume he/she knows his/her u(x,y) =x^0,5y^0,5 (Cobb-Douglas) (a) Find his/her optimal consumption given the income = 20, Px=2, Py=4! (b) Depict his/her optimal consumption graph! 2. Suppose that x and y (from your answer in number 1) are now perfect complement with u(x,y) = min(x,y). (a) Find his/her optimal consumption (given the same income and prices)! (b) Depict his/her optimal consumption graph!Felice lives and works for two periods. In the first period, she earns 520 coconuts and in the second period, she earns 570 coconuts. In each period, she pays 20 coconuts in taxes.a. Suppose that Felice can save or borrow from a bank at the same interest rate of 10%. Suppose also that she likes to consume today 240 coconuts. Draw herbudget constraint including both intercepts, her endowment point including its coordinates, and use an indifference curve to show her optimal consumption point and its coordinates.b. Suppose that the government cuts taxes by 10 coconuts. What will the government have to do to taxes in the future period to meet its lifetime budget constraint?c. What is the effect of the government’s action on Felice’s lifetime wealth, budget constraint and endowment point? Show and explain.d. What is the effect of the tax cut on her current consumption and welfare? Does the Ricardian equivalence hold? Explain!e. Now suppose that the economy enters a recession, and some…Please no written by hand solutions Data on before-tax income, taxes paid and consumption spending (on domestic goods and services) for the Simpson family in various years are given below. BEFORE-TAX INCOME ($) TAX PAID ($) CONSUMPTION SPENDING ($) 3000 3500 3700 4000 25 000 27 000 28 000 30 000 20 000 21 350 22 070 23 600 a. Graph the Simpsons's consumption function and find their household's marginal propensity to consume. b. How much would you expect the Simpsons to consume if their income was $32 000 and they paid taxes of $5000? c. Homer Simpson wins a lottery prize. As a result, the Simpson family increases its consumption by $1000 at each level of after-tax income. ('Income' does not include the prize money.) How does this change affect the graph of their consumption function? How does it affect their marginal propensity to consume?
- I need asnwers of d,e,f. Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?Suppose a consumer’s preferences over two goods x_1 and x_2 are given by u = Square root (X_1,X_2). Her income is M and the two goods cost p1 and p2 per unit respectively. a) Derive her utility at the optimal consumption point as a function of prices and income. b) Now suppose the government imposes a proportional tax t on the value of the good x_1 (such as VAT). If the consumer approaches the government for income compensation to remain as well off as before the tax (i.e. compensating variation in income), how much money would she ask for? c) If instead, the government decides to maintain consumer’s utility level not through lump-sum transfer but by introducing a proportional subsidy S on the price of good 2, then what should be the size of the subsidy? d) Based on your answer in part c) discuss how much would it cost for the government to introduce both a tax and a subsidy at the same time? Can you think of any situation when this policy would make sense?I NEED HELP WITH PART B! (a) A consumer has utility u(x,y,z) = ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz=1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? (HINT: MUx = 1/x, MUy= 2/y, MUz = 3/z and remeber the "equivalent bang for the buck" condition). (b) Forget about (a). Suppose you have t= 29 hours in total to spend on 3 projects X,Y and Z to make some money. If you spend x hours on project X, you make 2 sqrt(x) dollars; If you spend y hours on project Y, you make 3 sqrt(y) dollars; If you spend z hours on project Z, you make 4sqrt(z) dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x? on y? on z?