Naomi's expenditure function defined for a month for two commodities, Cassava (Q₁) and Banana (Q₂) is given by: [125P, PU 8 Where P₁ is the price of Cassava (P₁>0), P2 is the price of banana (P2>0) and U is the fixed utility. The income of Naomi is m, where m > 0. Derive the indirect utility function for Naomi (Hint: Use the duality conditions) Using the Shephard's Lemma condition, derive Naomi's Hicksian demand function for Cassava (Q₁¹). Using the Roy's identity, derive Naomi's Marshallian demand function for Banana (Q₂). Using the answer in (i), evaluate Naomi's maximum utility level when the price per i. ii. 111. iv. E =

Naomi's expenditure function defined for a month for two commodities, Cassava (Q₁) and Banana (Q₂) is given by: [125P, PU 8 Where P₁ is the price of Cassava (P₁>0), P2 is the price of banana (P2>0) and U is the fixed utility. The income of Naomi is m, where m > 0. Derive the indirect utility function for Naomi (Hint: Use the duality conditions) Using the Shephard's Lemma condition, derive Naomi's Hicksian demand function for Cassava (Q₁¹). Using the Roy's identity, derive Naomi's Marshallian demand function for Banana (Q₂). Using the answer in (i), evaluate Naomi's maximum utility level when the price per i. ii. 111. iv. E =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Rhea is determining how many gallons of milk (M) and loaves of bread (B) to purchase. Use the information in italics to answer the bolded question below: Rhea's marginal utility function for milk: MUN • Rhea's marginal utility function for bread: M = 0.5M-2 MUB = 0.5MB-1/2 • Rhea has $60 to spend on bread and milk. • The price of milk (Pm) is $3/gallon of milk. • The price of bread (Pb) is $1/loaf of bread. • For the sake of computation, assume that bread is the horizontal axis good (i.e., good X) and milk is the vertical axis good (i.e., good Y). When you set up the optimal budget decision rule for Rhea's consumer problem, which of the following statements best describes how much she will buy of both goods at her consumer equilibrium? O For each gallon of milk, Rhea will buy 1/3 loaf of bread. O For each gallon of milk, Rhea will buy 3 loaves of bread. For each gallon of milk, Rhea will buy 1 loaf of bread. O For each gallon of milk, Rhea will buy 6 loaves of bread.
Consider the following indirect utility function: V(p,I) = II,( Pi where E-1 a; = 1, and a; + 0 , Vi 1. What's the demand function for x;? (Hint: Take logarithm to both sides of the equation) 2. What's the original utility function? (Hint: If n is too abstract, let n = = 2)
Suppose that Evelyn’s utility function is given as: U(x,y) = xyEvelyn has an income of Php 100. For simplicity purposes, the prices of both goods are equal to one. Following the change in the price of good x, calculate the equivalent variation (EV). (Hint: Use the indirect utility function first to get the new utility level).
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5. Suppose the utility function is given by U(1,2)= 14 min{2z, 3y). Calculate the optimal consumption bundle if income is I, and prices are pi, and P2.
Question 2. You are given a utility function of three goods, K, L and M. U =U (K, L, M) = 10LogK + 5LogL + 2LogM %3D Where K, L and M are goods consumed. Furthermore, you are informed that the monthly salary is $500 and the prices per unit of K, L and M are $2, $10 and $4 respectively. Calculate the consumer's optimal bundle.
Philip's utility function is U(91, 42) = 8 (41) -0.45 92 Calculate the substitution, income, and total effects for a change in the price of q, on the demand for q1. The substitution effect for a change in P, is the income effect is and the total effect is (Round your responses to 2 decimal places and include a minus sign as necessary.)
3. The utility that Elena receives by consuming food F and clothing C is given by U(F, C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is £22. MUF = C+1 and MUc = F. (i) Define the term Marginal Rate of Substitution (MRS) (ii) Find the utility maximizing values of C and F for the numerical values given above (Hint: You can assume interior solution). (iii) Now suppose that price of C and Elena's income remain unchanged at £2 per unit and £22, respectively, while the price of F varies. Find the equation of the demand for F as a function of the unit price of F (PF).
c Serpil's utility function is U(B,C)= B · C , where B = veggie burgers per week and C = packs of cigarettes per week. a) What is her marginal rate of substitution if veggie burgers are on the vertical axis and cigarettes are on the horizontal axis? b) Serpil's income is $120, the price of veggie burger is $2, and that of a pack of cigarettes is S1. How many burgers and how many packs of cigarette does Serpil consume to maximize her utility? Illustrate your answers in a graph.
Find the expenditure function corresponding to utility function u(x₁,x₂) = ln(x₁ +a)+ln(x₂+b). a.e(p₁u) = 2√P₁P₂)eu/2 b.e(p,u)=e¹(√P₁P₂)+ap₁ + bp₂ Ⓒc. e(p₁u) = 2(√P₁P₂)eu/2-ap₁-bp₂ d.elpu)=e"√√P₁P₂
The price of a good changes. How could you calculate how much income the consumer would have to lose at the old prices to be as well off as they are at the new prices (equivalent variation)? Calculate the value of the expenditure function at the new prices and original utility minus the expenditure function at the original prices and original utility Calculate the value of the expenditure function at the new prices and new utility minus the expenditure function at the original prices and original utility Calculate the value of the expenditure function at the original prices and new utility minus the expenditure function at the original prices and original utility Calculate the value of the expenditure function at the original prices and original utility minus the expenditure function at the original prices and new utility Which of the following is NOT a good way to measure a change in consumer welfare from a price change? Find the equivalent variation Find the change in the value of…
Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers (C). Her market research has found that consumer demand for this product can beexpressed as a function of the price of the charger itself (PC), the price of phones (PF), andthe consmer’s income (I). Consumer demand can be described by the function C(PC, PF, I) =(i−10PC)/ (PF) Suppose her chargers come in all different capacities to meet any quantity demanded, so youdon’t need to worry about restricting C to whole numbers for this problem. (a) Does this product satisfy the law of demand?Explain.