1. Consider a market that consists of 50 consumers, i = 1, ..., 50, each with the following quasi-linear utility functionUi = mi + log x;over the numeraire good m (whose price is normalized to one) and x; units of good l; and 50perfectly competitive firms, j = 1, ..., 50, that produce good l. Each firm j produces q; unitsof good l using c; (q;) =i's endowment of the numeraire good is wi, i = 1, ...,50.•..q? /2 units of the numeraire good. Consumers are price takers, and(a) Derive the individual demand function, x; (p), and aggregate demand function, x (p), ofgood l.(b) Derive the individual firm supply function, q; (p), and aggregate supply function, q (p),of good l.(c) Find the equilibrium price p* and quantity q* of good l. What is each firm's profit?(d) Find each consumer i's equilibrium consumption of the numeraire m; as a function ofWi. Find the condition on w; that yields a strictly positive solution for m .*(e) Write down the equilibrium utilities u as a function of the initial endowments.

Since the question you have posted consists of multiple parts, we will answer the first three…

Answered: .. Consider a market that consists of…

.. Consider a market that consists of 50 consumers, i = 1, .., 50, each with the following quasi- linear utility function Ui = m¡ + log x;

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: Consider the following utility function: U=100X^0.75 Y^0.10. A consumer faces prices of Px = $5 and…

A: Given, U=100x0.85y0.10

Q: (3) Graph the demand curves associated with the utility function u(x, y) = x0-.25 ,0.75 and budget…

A: The demand(dd) function of a Cobb Douglas utility function with the following equation is given:…

Q: From economic theory, the willingness of a consumer to give up consumption of one commodity (X) in…

A: Consumer equilibrium refer to that situation of quantity consume where consumer receives maximum…

Q: A consumer's utility function is given by the expression: 0.8 U = (0.6X0.5 +0.4Y0.5) ². Determine…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: 6. Suppose that a fast-food junkie derives utility from three goods - softdrinks (x), 0.5 0.5…

A: Given, Utility Function: U(x,y,z)=x0.5y0.5(1+z)0.5 px=0.25py=1pz=2 Income (M) = 2

Q: 4. Show that the two utility functions given below generate identical demand functions for goods X…

A: Utility refers to the economic concept where individuals or consumers aim to make choices that…

Q: Let qA be the quantity of apples and go the quantity of oranges. A consumer's utility is described…

A: Consumer utility refers to the satisfaction or happiness that a consumer usually derives from the…

Q: Consider a consumer with the following utility function for goods X and Y: U(x,y) = 2 - 1 y А. What…

A: Marginal utility is that the added satisfaction that a consumer gets from having another unit of…

Q: The law of diminishing marginal utility states that.. price must be lowered to induce firms to…

A: Utility refers to the satisfaction derived from the consumption of good. The marginal utility shows…

Q: 2. Let your utility function be U (X, Y) = VX + VY. M This will give a demand function for X, X (Px,…

A: a. The demand function for Y is given by,…

Q: Q.7 A consumer's utility function is given by the expression: U = {0.6x"s + 0.4y"s). Determine the…

A: The marginal utility of a good or service is the change in the utility from an increase in the…

Q: Suppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the…

A: Demand curve shows the relationship between price and quantity demanded. It is derived from the…

Q: 1. A) When it comes to the level of utility that can be attained along an individual demand curve,…

A: 1 A) The answer is - a-the level of utility increases as the price of the product falls

Q: The law of diminishing marginal utility says that.... ........... as a person consumes more and more…

A: The consumers, or the individuals, or the households purchase goods, and services in order to…

Q: A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY =…

A: Given information: U=X1/2Y1/2 -------------> Utility function. Px = 10----------> price of…

Q: Let be following table of marginal utility data that you have been able to calculate for two goods…

A: Marginal utility is a fundamental concept in economics that describes the additional satisfaction or…

Q: Given the assumptions of the law of diminishing marginal utility (exactly the same product consumed…

A: Marginal utility (MU) is defined as the extra utility or benefit a consumer gets by consuming an…

Q: 3) Oğuz has the utility function U (X1,X2) = X:*x2?. (x:: nuts, x: berries). a) If Oğuz has 25 units…

A: Note: Since this question has five subparts, we are not allowed to answer more than three subparts…

Q: Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers…

A: ***Since the student has posted a question with multiple subparts, so the expert is required to…

Q: The utility function of a consumer is given as follows. U(x, y) = x?y3. MU, = 2xy and MU, = 3x?y?.…

A: Utility function of consumer:- U(x,y) = x2y3 MUx = 2xy3 MUy=3x2y2

Q: 1. Suppose the demand for frozen pizzas is given by the following equation: QD=100-50P+25P, -1.51…

Q: 1. A consumer has m dollars. The price of ₁ is p₁ dollars, and the price of P2 dollars. The consumer…

A: Utility function represents the relationship between utility and commodities or goods that are…

Q: a)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese…

A: Total customers = 120,000 Price of other products = Pm= $1 Price of Vietnamese Meals = Pv The…

Q: Select the function that represents the marginal utility of X for the utility function: U = X³Y².

A: Marginal utility ,it may be defined as the satisfaction that is derived from the consumption of an…

Q: Is the utility function u = min{3x, 2y + 1} a monotonic transfor- mation of u = min {3x, 2y}? True…

A: A monotonic transformation of a utility function is a transformation that preserves the order of…

Q: Consider the utility function u(x, y) = x1/2y1/2. How do the marginal utilities change as x…

A: Ans. Utility function u(x, y) = x1/2y1/2Take the partial derivative of the utility function w.r.t.…

Q: Suppose a consumer has a utility function given by U(X,Y)= MIN(X, 2Y). The consumer has $90 to spend…

A: Price Consumption Curve shows the optimal level of goods that can be consumed at various price…

Q: Khamzat consumes burgers (x1) and sodas (x2). Consider the CES utility function u(x1, x2) = (x? +…

A: Income effect: It refers to the effect under which there is change in the consumption of the…

Q: 2) Leyla has the utility function U(x₁,x₂) = 4x₁²x₂³. (x₁: nuts, x₂: berries). a) If Leyla has an…

A: In this question:- The utility function Ux1,x2=4x12x23 where x1 is nuts and x2 is berries Clearly in…

Q: Consumer satisfaction from consuming goods X and Y is as follows: U=10X+14Y-X2-Y2 and consumer…

A: Consumer equilibrium is the situation where he gets maximum satisfaction level of utility with given…

Q: Suppose we have a market with 200 individuals with preferences over two goods, x and y. 1. Consider…

A: Since you have posted multiple subparts, as per Bartleby guidelines, we can solve only the first 3…

Q: Given, the utility function is a Cobb-Douglas utility, u = x₁x), and budget m = pix1 + P2X2. a)…

A: The utility function represents the relationship between the utility and commodities consumed. Here,…

Q: A consumer has utility function U(q1, q2) min{4q1, q2}. Find the consumer's (Marshallian) %3D demand…

A: Given Utility function U(q1,q2)=min{4q1,q2} ... (1) Consumer income =y Price of good 1 =p1…

Q: The utility function of a consumer is given as follows. U(x, y) = x?y3. MU, = 2xy3 and MU, 3x?y2.…

A: It tells the inverse relation between quantity and price of the commodity.

Q: Bridget's preferences for apples( X) and bananas(Y) can be represented by the utility function…

Q: a) Choose X, and X, to max the utility fxn, '(X,X)=chX,+Q-Q}hX, st: M - P, X, + P,X; a) Write down…

A: Sorry as per our guideline we are only allowed to solve only 3 sub parts at a time kindly repost the…

Q: a) Choose X, and X, to max the utility fxn, U(X,X)=chX;+Q-a)h.X, st: M = P, X, + P,X; a) Consider a…

A: U( X1 , X2 ) = a ln X1 + (1-a) ln X2 M = P1X1 + P2X2 a.) Demand functions are derived by…

Q: Consider two consumers, A and B, who consume two goods, x and y. Assume that the utility function…

A: Utility function of A : U = xA yA3Endowment of A : x = 10 , y = 10 Price of x = Px , And Price…

Q: Question 2 Emma's daily utility function is U = 8√R+4M, where R represents the pounds of rice eaten…

A: Ans. 2. Emma's utility maximization level is where the slope of the indifference curve is equal to…

Q: Suppose there are 2,000 potential consumers in the Chestnut Hill market for tablet computers. All…

Q: 2. Suppose John's utility function is UX,Y) = 4VXY , where X is consumption of beer and Y is…

A: A good has diminishing marginal utility when marginal utility decreases with increase in units of…

Q: Graph the demand functions of the two goods (price as a function of quantity) assuming the…

Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

1. Consider a market that consists of 50 consumers, i = 1, ..., 50, each with the following quasi-
linear utility function
Ui = mi + log x;
over the numeraire good m (whose price is normalized to one) and x; units of good l; and 50
perfectly competitive firms, j = 1, ..., 50, that produce good l. Each firm j produces q; units
of good l using c; (q;) =
i's endowment of the numeraire good is wi, i = 1, ...,50.
•..
q? /2 units of the numeraire good. Consumers are price takers, and
(a) Derive the individual demand function, x; (p), and aggregate demand function, x (p), of
good l.
(b) Derive the individual firm supply function, q; (p), and aggregate supply function, q (p),
of good l.
(c) Find the equilibrium price p* and quantity q* of good l. What is each firm's profit?
(d) Find each consumer i's equilibrium consumption of the numeraire m; as a function of
Wi. Find the condition on w; that yields a strictly positive solution for m .
*
(e) Write down the equilibrium utilities u as a function of the initial endowments.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Ans. (a)

Ans. (b)

Ans. c

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

The utility of a consumer derives from consuming the two goods X and Y can be assumed to be determined by the utility functionU(X,Y)= 4X03Y05. If good X costs 10 birr a unit and good Y costs 15 birr a unit and the consumer's income is 120 birr. What combination of X and Y that will maximize utility?
Show that the two utility functions given below generate identical demand functions for goods X and Y UCXY) log(X)+log(Y C) UCxY) (XY05 The demand function for good X and the demand function for good Y for both utility functions equal O A. X= and Y Pv Px О В. Х- and Y 2Pv Ос. X Y= 21 PXPY O D. Х- and Y 2P. 2Py ОЕ. X= Y= РХPY
The term “law of diminishing marginal utility” used in explaining downward sloping demand curves, others things constant, is best described by which of the following statements? The total satisfaction you obtain from consuming a good tends to fall. The average satisfaction you obtain from consuming a good tends to fall. The additional satisfaction you obtain from consuming an additional unit of a good tends to fall. The total satisfaction you obtain from the good tends to rise.
Hello, I am not understanding this practice problem. I dont know how to solve the second half .
Given the utility function Log Y = 0.42logX1 + 0.58logX2 Find the demand function
2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences over these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where x represents the number of cans of soda and y represents the number of juice boxes. a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y). b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda and juice. Write Ping's demand curve for juice (y). Illustrate his demand curve. c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and $30, resp.). Use your demand functions to find his best bundle. In an indifference curve diagram illustrate his best bundle at these prices. For the remainder of the question assume that Ping's allowance (income) rises to $36 per week and the prices of the two goods are unchanged at Px= $1.5 and Py= $1. d) Use your demand functions to find his new best bundle. e)…
10
1/2 Consider a consumer with the utility function u(x, y) = 2x¹2 + y, an income of I = Rs 100, and price of good y is Rs 1. A) Find the demand functions for goods x and y. B) If, ceteris paribus, price of good x decreases from Rs 4 to Rs 3, what is the compensating variation? 1.
8
Let U(x, y) = 3x + y be the utility function of a consumer, whohas a budget of I. As a function of I, find the consumer’s Walrasian demand when the prices are px = py = 1. The price of good x increases to 2, find the new Walrasian demand for the new prices px = 2 and py = 1. Decompose this change into an income and a substitution effect.
For each of the following utility functions answer the following questions (i-iv): i) Calculate the marginal utilities MUx and MUy ii) Calculate MRSx,y and determine if this is diminishing as good x increases iii) if I=80, Px= 4, Py=2, determine the utility maximizing basket. iv) Determine the demand curves for good x and y (a). u(x,y)= 6x^2/3 +2y (b) u(x,y)= 3x+7y
Given the utility function, where U is the total utility and x and y are the commodities consumed, find the marginal utility function of each of the two commodities.