Chino has a quasi-linear utility function given by U(x1, X2) = x₁ + 6x2, where prices of goods 1 and 2 are given by p₁ and p2, respectively. If Chino's budget is given by m, • Solve for the utility-maximizing quantities of x₁, x2, and > • Find the maximum utility. • Show that the change in maximum utility due to a peso change in income m is equal to the La- grange multiplier you got in the first bullet.

Chino has a quasi-linear utility function given by U(x1, X2) = x₁ + 6x2, where prices of goods 1 and 2 are given by p₁ and p2, respectively. If Chino's budget is given by m, • Solve for the utility-maximizing quantities of x₁, x2, and > • Find the maximum utility. • Show that the change in maximum utility due to a peso change in income m is equal to the La- grange multiplier you got in the first bullet.

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

Q4 Michael spends all of his money on yams and pudding. His utility function is y.5 2p.5, p.5 24.5) Op = = O p Op = = = Using the typical budget constraint (I = Pyy + Ppp) which of the following is his demand function for pudding? Reminder: 5 = √√√x 2P₂ U=p5y5 (MUp = Pp O None of the above MU, =
= Suppose you are trying to minimize your expenditures E utility level (20.5 + x9.5)² = 175. 4x1 + 3x2 subject to the target maximum • Set up the Lagrangean function for this expenditure-minimization problem with constraint • Compute for the expenditure minimizing quantities of ₁ and ₂. x2. • What is the minimum expenditure you can incur given the level of utility you have to attain?
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 ?
Consider a consumer with income M, who can buy good 2₁ at price p₁ per unit and can buy good x2 at price p2 per unit. Consider a budget constraint diagram for this consumer, with quantity of good *1 measured along the horizontal axis and quantity of good 2 measured along the vertical axis. If p₁ increases and p2 increases (though not necessarily by the same percentage), while M remains unchanged, which of the following changes to the consumer's budget set definitely occur? The budget line slope becomes steeper The budget set becomes strictly larger None of these changes necessarily occur The budget set becomes strictly smaller O The budget line slope becomes flatter
Darwin consumes cigarettes (x1) and other goods (x2). His preferences are given by UD(q1,q2)=4lnq1 +q2The quantity of good 2 is measured in units of income and so you can assume that throughout this problem, the price of good 2 is normalized p2 = 1 (a) Using the Lagrangian, derive Darwin’s uncompensated demand for cigarettes: D1D(p1,Y). Note that we are holding p2 =1 and so that is not a variable in the demand function. Using the Lagrangian, derive the equation λ∗(p1, Y ). Provide an economic interpretation of the Lagrange multiplier. Does it vary with income, Y ?
Suppose that there are two goods, gl and g2, that Jane consumes. Demand functions for these two goods are given as follows: gl * = gl(pg1), pg2 ,Inc) g2 * = g2(pg1), pg2 ,Inc) where pg1, pg2 ,Inc refer prices of the goods and income, respectively. Explain and demonstrate (on the graph) the substitution and income effect for both an increase and decrease in price good g1. Use the notations given in the question.
Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 4[A-4 + B-4-4 + 40. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EV
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.
Suppose you are given the following information for a particular individualconsuming two goods, a and b: Pa = $5, Pb = $6, MUa = 100, MUb = 200, and income (m) = $200.a) Sketch the budget set. What is the slope of the Budget Line? What are maximal possibleconsumptions of a and b?b) What is the MRSab for the two goods?c) Is this person maximizing her utility? How can you tell?d) Should she consume more of good a or of b? Explain.e) Why can’t you tell what her optimal bundle is? Explain.
- Assume an individual has quasilinear preferences of the form U(x1,x2) = 3x1¹2 + 2x2. If the price of Good 1 is $1 and the price of Good 2 is $2, how many additional units will the individual consume of Good 2 if her income increases by $1, assuming we're at an interior optimum? A. B. C. D. The individual's consumption of Good 2 will increase by 1/2 unit. The individual's consumption of Good 2 will increase by 1 unit. The individual's consumption of Good 2 will decrease. The individual's consumption of Good 2 will not change.
Derive Ryan's demand function for q₁, given his utility function is where o = = (9₁) P + (9₂)P, 1 1-p The demand curve for q₁ as a function of P₁, P2, and Y is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ 9₁ = character.) U= Let the price of q₁ be p₁, let the price of q2 be p2, and let income be Y.
A consumer's utility function is given by u (r_y) := r'/2y}/2 for any nonnegative x and y, representing the consumption quantities of goods x and y, respectively. Suppose that the price of good y is constantly ¢1, and that the consumer is given income m cedis (and nothing else). Denote p, for the price of good r. Based on the quantity demand (p, m) for good r. a. Given that p, > 1/(4m), calculate i (Pz, m) and (Pz, Py, m), then use the Slutsky equation to deduce what the substitution effect r° (pz, y) is equal to. b. Given that p, < 1/(4m), calculate i (P, m) and i (P2, Py, m), then use the Slutsky equation to deduce what the substitution effect r° (Pz; y) is equal to. c. What is your interpretation of the your result in a and b above?