Consider a utility maximizing consumer who generates utility according to the following utility function: U=In(k)+s where k is the quantity of masks consumed and s is the quantity of hand sanitizer consumed. Let the price of k, the price of s, and income be noted as Pk Ps, and M, respectively. * Set up the utility maximizing Lagrangian and derive the Marshallian demand functions. What is the quantity demand of k and s if income = $120 pk = $2 and ps = $12? Derive the indirect utility function and the expenditure function. Use Shephard's Lemma to derive the compensated (Hicksian) demand curves.

Consider a utility maximizing consumer who generates utility according to the following utility function: U=In(k)+s where k is the quantity of masks consumed and s is the quantity of hand sanitizer consumed. Let the price of k, the price of s, and income be noted as Pk Ps, and M, respectively. * Set up the utility maximizing Lagrangian and derive the Marshallian demand functions. What is the quantity demand of k and s if income = $120 pk = $2 and ps = $12? Derive the indirect utility function and the expenditure function. Use Shephard's Lemma to derive the compensated (Hicksian) demand curves.

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

PROBLEM 2 – Uncompensated and Compensated Demand Functions, Price Elasticities of Demand, and Expenditure Functions Susi enjoys her favorite drink (D) and food (F) which she always spends her monthly income on those goods. Her average allocated income spent on drink and food is Rp 3 million, and the current prices of drink and food are Rp 30k and Rp 90k, respectively. Suppose her happiness by consuming those goods can be capture by the utility function as follows: *see image* a. What are her uncompensated (Marshallian) demand functions for drink and food, and calculate how many drinks and food that she currently consumes? Draw and describe how her demand curves for drink and food are shifted by changes in her income or the price of the other good. (hint: Use Lagrangian method). b. If the price of drink increases to Rp 50k, calculate the price elasticity of demand for drink. c. What is her the expenditure function for drink and food? Use the expenditure function to compute the…
Consider a consumer with indirect utility function v(p, w) = w - B1p1 - B2p2 √P1P2 where 3₁ and 32 are nonnegative constants. (a) Find the consumer's expenditure function. (b) Find the Hicksian and Marshallian demands for Good 1. (c) Find expressions for the substitution and income effects on Good 1 associated with a marginal increase in the price of Good 2. (d) Suppose that the price of good 1 changes from pi to kp₁ where 0 < k < 1. Find the compensating variation of this price change.
Consider the following Marshallian Demand Function derived from the utility maximization problem, X = a M P where X is the quantity consumed, Mis income of the consumer, P is the price of the good, and α is some number between 0 and 1 which represents the relative importance of the good. Does this demand function satisfy the law of demand? (_ Why or why not? (*
What is the demand for goods L and Y given the utility function U(L,Y) = L+2Y where the price of L is $1 dollar per unit and the price of y is $Z per unit.
Question 1. Assume that consumer has the following demand function for good X m x1 = 10+ 10р1 If income is 200 and product is sold for price of 10, find subsitition and income effect in case of new price of 6 dollars. Show it on the graph as well.
Suppose that an individual has a Utility function represented by a CES function. The utility function of the individual is given as: U(x,y) = x1/2 + y1/2 b. Calculate the own price elasticity using the "share elasticity" of any good. Let us assume that the prices of both goods are equal.
Joan has the following utility function: u(x, y) (a) Find Jane's marshallian demands. 5x + 3y.
Suppose that i's preferences over goods x and y are represented by the following utility function U₁(x, y)=x45¹5. Let m denote the consumer's income, p denote the price of good x and let the price of good y equal 1. A) Find the Marshallian demand functions for goods x and y. B) Show how each of the demand function is affected by a change in the price of good x. C) Which of the goods is an inferior good?
Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand Functions
Suppose a consumer purchases food X and clothing Y. The utility function of the consumeris given by: U(X,Y ) = XY + 5Y and the budget /income/ of the consumer is 200 ETB. Andalso the price of food is X P and the price of clothing is Y P . Then drive the equation ofconsumer’s demand function for food and clothing.
Derive the expenditure function for the consumer and the hickson demand function
3. Consider the following model. U(X,Y)= X2$Y35 Px =2 Py = 3 I= 100 Suppose price of X changes to Px= 4. What are the substitution effect and income effect on Y?