Consider the following utility function:U = 100x.50,0.50A consumer faces prices of P, = $2 and Py =$1.Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X anunits of good Y. Then the marginal rate of substitution is equal to:MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.)Use absolute values.The consumer should consumeto maximize utility.more Y and less Xthe same amount of X and Ymore X and less Y15tvMacBook Air80escDIIF1F2F3F4F5F6F7F8@#3%278.QWEYtabs lockASFGHJZCVNMOnteel8 :< COTD

U=100X^0.5Y^0.5 Px=$2 Py=$1 MRS=1.83 MRS is the ratio of marginal utilities of the two goods In a…

Answered: Consider the following utility…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P, =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y O étv MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 F8 # $ % & 1 2 7 Q W E T Y tab S D F G caps lock C V M ft control option command つつエ B N
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…
Consider an individual with preferences represented by the following utility function: U (x1, 12) = x{x; The individual faces prices: P1 = 0.5; p2 = 1 And has income: M = 250 If the price of good one increases to p1 =1 For this change in price, mark all of the following answers that are correct. (EV = equivalent variation; CV = compensating variation) O In absolute value, EV is greater than Cv O In absolute values, change in Consumer surplus is smaller than CV. O In absolute value, CV is greater than EV In absolute values, change in Consumer Surplus is smaller than EV. There is not enough information to determine an answer.
Consider the following utility function: U = 100x°.50,0.50 A consumer faces prices of P, = $2 and P, =$1 Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. 15 stv МacВook Air 80 DI esc F1 F2 F3 F4 F5 F6 F7 F8 @ %23 2$ & 1 2 4 6 7 8 Q W T Y tab A S F H J K aps lock C V M control option command B H
3. Consider a consumer with the following Cobb-Douglas utility function U(x, y) = x¹/3y2/3 Assume that the consumer faces a price of $1 for y, and a total income/budget of I. The price of z is left unrestricted as pr (a) Find the marginal rate of substitution, MRS, for this consumer. (b) Set up this consumer's utility maximization problem and find demand for 2 and y. (c) Solve (or rework) for income/budget I, in order to obtain the Engel curve of a. Is the slope of the Engel curve positive? Interpret: is the good normal or inferior?
Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…
3. A canonical utility function. Consider the utility function u(c) 1-σ where c denotes consumption of some arbitrary good and ơ (Greek lowercase letter sigma") is known as the "curvature parameter" because its value governs how curved the utility function is. In the following, restrict your attention to the region c> (because "negative consumption" is an ill-defined concept). The parameter σ is treated as a constant. Plot the utility function for ơ-0. Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? Plot the utility function for ơ marginal utility? Is marginal utility ever negative for this utility function? Consider instead the natural-log utility function u(c)=In(c). Does this utility function display diminishing marginal utility? Is marginal utility for this utility function? Determine the value of σ (if any value exists at all) that makes the general utility function presented above collapse to the…
Consider the following utility function: U= 4X + Y. A consumer faces prices of P, = $2 and P, =1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 10 units of good X and 19 units of good Y. Then the marginal rate of substitution (MRS) is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) étv Help Me Solve This eText P MacBook Air 80 DII esc F2 F3 F6 F8 F1 F4 F5 F7 @ 23 2$ & 1 2 4 6 7 8. Q W E R T Y U tab A S G caps lock C V shift fn control option command ーのエ B レ

4.13 CES indirect utility and expenditure functions In this problem, we will use a more standard form of the CES utility function to derive indirect utility and expenditure functions. Suppose utility is given by U(x, y) = (x° +y®)'/8 [in this function the elasticity of substitution o = 1/(1 – 6)]. a. Show that the indirect utility function for the utility function just given is V = I(p, + p,)¬/", where r = 8/(ò – 1) = 1 – 0. b. Show that the function derived in part (a) is homogeneous of degree zero in prices and income. c. Show that this function is strictly increasing in income. d. Show that this function is strictly decreasing in any price. e. Show that the expenditure function for this case of CES utility is given by E = V(p', + p,)''". f. Show that the function derived in part (e) is homogeneous of degree one in the goods' prices. g. Show that this expenditure function is increasing in each of the prices. h. Show that the function is concave in each price.
You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.
The goods in the next question are not ale and bread. To solve this question, you are going to have to evaluate the condition The price p is defined for you, but you will have to define the marginal rate of substitution for yourself. What ratio of marginal utilities should you use? You will know the answer to this question once you have defined the marginal rate of substitution – that is, decided which good is being given up and which good is being given in compensation. When making this decision, remember that both sides of this equation refer to the same kind of trade. The right-hand side describes the rate at which one good can be traded for the other in the marketplace; and the left-hand side describes the rate at which someone is willing to trade that good for the other. Thus, the definition of the price determines the manner in which the marginal rate of substitution must be defined. Pierre lives on red wine and blue cheese. His utility function is. where w is his…
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 (x2) 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 (x2) consumption for Megan with the tax.

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