2. **Symbolic Consumer Choice:** Patrick lives in a simple world where there are only two consumer goods, french fries (f) and kolbassa (k), both of which align well with his interests. Patrick’s preferences over possible bundles of french fries and kolbassa are given by the utility function: $ U(f, k) = 2f^{0.5} k^{0.5} $. The prices of a frisbee and of a kabob are $ p_f $ and $ p_k $. a. **Graph Patrick’s budget constraint** with french fries on the x-axis and kolbassa on the y-axis. What is the marginal rate of transformation (MRT)? In no more than two sentences define an MRT and explain conditions under which it would get steeper. b. **What is the marginal rate of substitution (MRS)?** Define it in no more than two sentences and calculate it. c. **Consider two simple positive monotonic transformations of Patrick’s utility function.** The first is $ U(f, k) = fk $. The second $ U(f, k) = \ln f + \ln k $. Calculate the MRS for each of these transformations and explain in no more than two sentences why these transformations do not change the MRS's. d. **Let’s grind out the solution with the substitution method.** First, carefully write out the problem Patrick must solve to maximize his utility. Because we know that all of the utility functions considered will give the same answer in terms of MRS = MRT, use the natural log version of the utility function from part (c). e. **Now using the substitution method to solve** for Patrick’s utility maximizing quantities of french fries and kolbassa, $ f^* $ and $ k^* $, respectively.

Consumer choice refers to the decision-making process that individuals or households go through when…

2. Symbolic Consumer Choice: Patrick lives in a simple world where there are only two consumer goods, french fries (f) and kolbassa (k), both of which align well with his interests. Patrick's preferences over possible bundles of french fries and kolbassa are given by the utility function: U(f,k) = 2f0.5 40.5. The prices of a frisbee and of a kabob are pf and Pk. a. Graph Patrick's budget constraint with french fries on the x-axis and kolbassa on the y-axis. What is the marginal rate of transformation (MRT)? In no more than two sentences define an MRT and explain conditions under which it would be get steeper. b. What is the marginal rate of substitution (MRS)? Define it no more than two sentences and calculate it. Consider two simple positive monotonic transformations of Patrick's utility function. The first is C. U(f, k) = fk. The second U(f, k) = lnf + lnk. Calculate the MRS for each of these transformations

2. Symbolic Consumer Choice: Patrick lives in a simple world where there are only two consumer goods, french fries (f) and kolbassa (k), both of which align well with his interests. Patrick's preferences over possible bundles of french fries and kolbassa are given by the utility function: U(f,k) = 2f0.5 40.5. The prices of a frisbee and of a kabob are pf and Pk. a. Graph Patrick's budget constraint with french fries on the x-axis and kolbassa on the y-axis. What is the marginal rate of transformation (MRT)? In no more than two sentences define an MRT and explain conditions under which it would be get steeper. b. What is the marginal rate of substitution (MRS)? Define it no more than two sentences and calculate it. Consider two simple positive monotonic transformations of Patrick's utility function. The first is C. U(f, k) = fk. The second U(f, k) = lnf + lnk. Calculate the MRS for each of these transformations

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

Suppose you had a budget of $20.00 and the prices of a burger and a slice of pizza are $5.00 and $2.00 respectively. What would be your optimal consumption bundle?
Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.
27. Mike spends all his income on films (F) and concerts (C). Films cost $10 and concertscost $30. Mike’s preferences can be described by the utility function: U = F C and hence themarginal utility of films is C and the marginal utility of concerts is F. Which of the followingbundle will Mike purchase? (Hint: You do not need to know income in $ amount. Answerthe question using the tangency condition.)(a) Mike purchases 30 concerts and 10 films a month.(b) Mike purchases 10 concerts and 30 films a month.(c) Mike purchases 20 concerts and 20 films a month.(d) Mike purchases 5 concerts and 10 films a month.
2. Utility function: U(X,Y)= 2XY* Budget Constraint: 2X +4Y = 80 a. Calculate the utility maximizing amount of X and Y.
4.
2. Vibha consumes three goods X, (shirts), X, (food in pounds), and X, (shelter in square feet). Vibha's utility function is given by: U (X,, X, X,) = 5ln Xt 3ln X + 2ln X, where In (x) or log. (x) is the natural logarithm. Vibha's weekly income is $100. Let the price of X, = P, = $10, the price of X, = P, = $2, and the price of X, = P; = $4. What is the equation for Vibha's budget constraint? а. b. |How many shirts, pounds of food, and square feet of shelter, will Vibha consume, as a rational consumer?
1. Sam is going to Baltimore for the day to watch his favorite baseball team (Orioles). Sam loves his Orioles, but he is addicted to drinking beer (B) and eating hotdogs (D) while watching his team. His utility function is: U = (B*D)1/2 a. Suppose Sam has $50 to spend on beer and hotdogs. Beer costs $5 a mug and a hotdog costs $4. Draw Sam's budget constraint. b. Suppose Sam spends all of his income on beer. How many mugs of beer can he buy? What is his utility? c. Will Sam's income allow him to reach a U = 5? d. If Sam buys 4 hotdogs, how many mugs of bear can he buy? What is his utility? e. What is the combination of beer and hotdogs that yield the highest utility? 2. Firm A's Price $20 $15 $20 $40 profit $35 profit Firm B's Price $37 profit $39 profit $15 $49 profit $38 profit $30 profit $35 profit a. Firms A and B are member of an oligopoly. Which solution will Firm A and B select? b. Is there a Nash equilibrium? If so, what is it? c. Which solution will Firm A and B select if Firm…
1. Suppose you are considering to make a decent holiday dinner. In this year, to be creative, you are thinking to put Copper River Salmon from Alaska (fillet) and fresh Atlantic Lobsters from Maine as entrée on the table. Use the information given, to finish the questions below. (1) The table following provides you total utility (U) and marginal (MU) from consuming Salmon and Lobster. Suppose your total utility of Salmon consumption (U1) is a function of the units (Q as pound or lbs.) of salmon consumed, as U1 =. =/400Q. Similarly, your total utility of Lobster (U2) has the form as units (Q as lbs.) of lobster consumed, which is U2 = /36Q + 40. Now fill the empty spots in the table using the information given. Total utility and marginal utility of Salmon and Lobster. Copper River Salmon Atlantic Lobster Q (Ibs.) U1 MU1 U2 MU2 1 20.00 20.00 8.72 8.72 2 3 4. 6. 7 8 10 (2) With a certain amount of budget, you are going to purchase both Salmon and Lobsters. To maximize your total…
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.
I. You only consume two goods and your preferences are represented by utility function 2 U(x₁, x₂) = (x1.5 + x2.5) for x₁ > 2 and x₂ > 0.
Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $1,000 and can buy apples at $10 per pound and kumquats at $10 per pounc utility function is U(a, k) = 4a + 3k. What is his marginal utility for apples and his marginal utility for kumquats? Andy's marginal utility for apples (MU) is MU, = and his marginal utility for kumquats (MU) is MU, = (Enter your responses as whole numbers.) What bundle of apples and kumquats should he purchase to maximize his utility? Andy should consume apples and kumquats. (Enter your responses as whole numbers.) React tv MacBook Air 80 DI DD F1 F2 F3 F5 F6 F7 F8 F9 F10 @ #3 $ % & 1 2 4 7 8. 9 Q W E Y { A S F G H. J C V M ption command command option .. .. V B
Kyle's utility function is U = 2.7X +2.7Y, where X is units of good X and Y is units of good Y. What is the marginal utility of good X? O 3.7 3.7X + 3.7 O 2.7