A consumer has the utility function U(x1,x2) = min{2x1,x2} and an income of $200. Initially, the price of good 1 is $6 and the price of good 2 is $2. a) Find consumer's demand function for good 1. b) Then, price of good 1 decreases to $ 4 and price of good 2 stays at $2. What is the total change in demand for good 1? Show the income and substitution effects of this price change both graphically and algebraically.

A consumer has the utility function U(x1,x2) = min{2x1,x2} and an income of $200. Initially, the price of good 1 is $6 and the price of good 2 is $2. a) Find consumer's demand function for good 1. b) Then, price of good 1 decreases to $ 4 and price of good 2 stays at $2. What is the total change in demand for good 1? Show the income and substitution effects of this price change both graphically and algebraically.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section6.A: Indifference Curve Analysis

Problem 15SQ

See similar textbooks

Similar questions

A consumer has the following demand function for good 1: x1 = (1/4)(m/p1) The original price of the good is $2 and the consumer’s income is $200. Calculate the substitution effect, the income effect and the total effect for this consumer, when the price of good changes to $1.
Suppose a consumer has a utility function given by U(X,Y) = MIN(X, 2Y). The consumer has $90 to spend (M = $90). The Price of good Y is Py = $1. a) Draw the consumer's Price Consumption Curve for the following prices for good X: Px = $1, Px = $2, Px = $2.5. For each set of prices, make sure to accurately draw each budget constraint, and also identify the consumer's optimal bundle on each budget constraint. Make sure your graph is neat, accurate, scaled properly, and fully labeled to receive full credit.
Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.
Suppose that Sam has a utility function u(x, y)= x+y where x is the amount of good 1 and y is the amount of good 2. The price of good 2 is $20, and the income is $ 90. With the $5 price decrease of good 1 from $10 to $5, then what is the substitution effect and income effect on the demand for good 1?
Chiara has the utility function U(x1,x2) = x1(x2+5). The price of x1 is 5$ and the price of x2 is 2$. Income is 25$. A)How much of each good does Chiara demand? (without lagrangian) B)If Chiara’s income doubles, but prices remain unchanged, will Chiara’s demand double? C)How does ordinary demand change when income doubles (50$) and the price of x2 also double?
If the consumer's utility function is given by U(x, y) = 10x0.5 0.5, solve for the optimal quantity of good that the consumer should purchase if the price of good a is $10, the price of good y is $5, and the consumer has $40 of income. (Note that your solution should be a whole number)
Ambrose's brother Anthony has an income of $75 and a utility function U(x1, x2) = 20x1/21 + x2. The price of good 1 (nuts) is $2 and the price of good 2 (berries) is $1. How many units of nuts will Anthony demand
David's utility function for good X and Y is given by U (X,Y) =X2y3. Where px,py and I are the price of good X, price of good Y and consumer income respectively. A. Write the budget constraint of the consumer and derive the demand function for good X and Y b: What combination of X and Y maximizes the consumer at I=100,px=4,and py=5 c. Calculate the marginal rate of substitution between X and Y at equilibrium and interpret your results.
Bob has utility function U(x,y)=x2+y over goods x and y a) Do we have a name for this type of utility function? Are Bob's preferences well-behaved? b) Let Bob have budget I=$60, and let prices be Px=$30, Py=$10. Find Bob's optimal basket of goods x and y. Is this an interior or corner solution? c) What will happen if the price of good y doubles? [Think about: can we use this utility function to describe preferences over pet snakes and pet mice?]
Consider the following utility function that expresses the preferences of any consumer for good x and good U(x, y) Min {2x, y) Consider that the price of x is $4, the price of y is $2, and the income R is $100. Reply: a) What is the marginal rate of substitution for x? b) What is the marginal rate of substitution for y? c) What is the expression of demand ( demand function) of x? d) What is the demand expression (demand function) for y? e) What is the basket composition that maximizes this consumer's satisfaction given the given restriction? f) What is the utility achieved with this basket?
Part 1: Ambrose's brother Anselm has an income of $265 and a utility function U(x1,x2)=70x^1/2 + x2. The price of good 1(nuts) is $5 and the price of good 2 (berries) is $1. How many units of nuts will Anselm demand? Part 2: Ambrose's brother Augustine has an income of $128 and a utility function U(x1,x2)=36x^1/2 + x2. The price of good 1(nuts) is $3 and the price of good 2 (berries) is $1. How many units of berries will Augustine demand?
Suppose you consume x1 unit of Goods 1 and x2 units of Goods 2, the utility you get is U(x1, x2) = x1x2, the price of Good 1 is $3, the price of Good 2 is $5, you have a total of $30. How many units of Goods 1 and 2 will you consume?