Suppose the utility function for an individual is given by u(x, y) = x + y, where x and y are two...
Question:
Suppose the utility function for an individual is given by {eq}u(x, y) = x + y {/eq}, where {eq}x {/eq} and {eq}y {/eq} are two goods. The budget constraint of an individual is {eq}2x + 5y = 10 {/eq}, where {eq}I = 10 {/eq} is the income of an individual, {eq}P_x = 2 {/eq} - the price of good {eq}x {/eq}, and {eq}P_y = 5 {/eq} - the price of good {eq}y {/eq}. Suppose the individual wants to make {eq}u(x, y) {/eq} as high as possible.
A. What would be the demand for {eq}x {/eq}?
B. Suppose the price for {eq}y {/eq} is now 1, i.e. {eq}P_y = 1 {/eq}. What would the total demand for {eq}x {/eq} be? What can be said about {eq}x {/eq} and {eq}y {/eq}?
Substitute Goods:
The types of goods that can be used in place of each other are known as substitute goods. The substitute goods have a direct relationship between each other. In other words, if the price of one good increase, the quantity demanded of the other good also increases.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerGiven:
{eq}\begin{align*} u\left( {x,y} \right) &= x + y\\ 2x + 5y &= 10 \end{align*} {/eq}
A) The utility function is perfect substitutes...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:

from
Chapter 8 / Lesson 13Understand what substitute goods are by learning the substitute goods definition. Discover some examples of substitute products. Understand the substitution effect.
Related to this Question
- An individual has the utility function a) Find his consumption on x_1 and x_2 when his budget constraint is 3x_1+4x_2=100. b) Year later his budget constraint is 3x_1+2x_2=100, find his consumption
- Suppose an individual consumers two goods, with utility function U (x1, x2) = x1 + 6{\sqrt{x1x2 +9x2 Formulate the consumers utility maximization problem when she faces a budget line p1x1 + p2x2
- Suppose there is an economy with two individuals, A and B, and two goods, X and Y. The individuals' utility functions are: UA = 0.2lnX + 0.8lnY, UB = 0.8lnX + 0.2lnY For simplicity, let the price of
- Suppose that an individual with an income ''I'' cares about two goods, X and Y. The price of the two goods is Px and Py. The individual has the following utility function: U(X, Y) = X(2+Y) a) Find the Marshallian(uncompensated) demand for X and Y. b) Fi
- Suppose a consumer has an income of $30 that is spent on two goods: X and Y. The price of good X is $1.00 and the price of good Y is $3.00. Which of the following bundles of X and Y lie on the individual's budget constraint? a. 8X and 6Y. b. 6X and 8Y. c.
- Suppose a consumer has an income of $30 that is spent on two goods: X and Y. The price of good X is $3.00 and the price of good Y is $1.00. Which of the following bundles of X and Y lie on the individual's budget constraint? a. 8X and 6Y b. 6X and 8Y c. 8
- Suppose Vivian has a utility function of U = X^{0.4}Y^{0.6}, where X and Y are two goods. The prices for X and Y are $4 and $6, respectively. She has $100 in her pocket. Write down Vivian's budget constraint to buy both goods.
- An individual has a utility function given by: U = 2XY Income is $120, Px = $4 and Py = $1. Suppose that the price of X falls to Px = $3. a. Calculate the gain in consumer welfare using the equivalent variation measure when the price falls. b. Calcula
- Consider an individual making choices over two goods x and y with prices p x and p y with income I and the utility function u x y 2 x y Find the compensated Hicksian demand for x
- Suppose there are two goods, X and Y. The utility function for these goods is given by U(X,Y) = 5X+2Y. Suppose I had $50 to spend on these two goods. Good X has a price of $5 per unit, while the price
- Suppose a consumer's utility function is given by U(X, Y) = X*Y. Also, the consumer has $360 to spend, and the price of X, P_x = 9, and the price of Y, P_y = 1. a) How much X and Y should the consume
- A consumer has a utility function U(X, Y) = X^{1/4}Y^{3/4}. The consumer has $24 to spend and the prices of the goods are P_X = $2 and P_Y = $3. Note that MU_X = (1/4)X^{-3/4}Y^{3/4} and MU_Y = (3/4)X^{1/4}Y^{-1/4}. Draw the consumer's budget constraint a
- A household has the budget constraint y = px1 + x2 where the price of good is normalized to one. The utility function is given by: U(x1, x2) - Min (x11, 4x2) Solve the demand function x1 and x2 and utility U(x1, x2) as functions of y and p.
- Consider a consumer who consumes only two goods, x and y. His utility over these two goods is given by U (x, y) = x + y. The budget constraint of the consumer is given by 3x + 6y = 300, where 3 is the price of good x, 6 is the price of good y, and 300 is
- Suppose a consumer maximizes the utility function U=ln (xy) subject to the budget constraint 4x +2y =12. Find the consumption bundle (x*,y*) that maximizes utility for the consumer.
- Suppose that John has the utility function u(x, y) = 3x^{\frac{1}{2 + y. Suppose that the budget equation is given by P_xx + P_yy = M. Suppose that the price of a unit of x is 1 and the price of a unit of y is 2 and John's income is 8. Find how many uni
- A consumer faces a utility function defined as U ( X ? Y ? ) and has a budget constraint represented by M = P x X + P y Y . Find the consumers equilibrium
- Suppose a consumer's utility function is given by U(X,Y) = X^ 2 \times Y. The Price of Y is P Y = 3, and the consumer has M = $18 to spend. Draw the Price Consumption Curve for the following values of P_x: P_x=1, P_x =2, P_x=3.
- A consumption bundle that lies inside the individual's budget line is a consumption bundle that: A) does not maximize the individual's utility given their tastes, income, and the price of the goods. B) does not exhaust the individual's income. C) the indi
- Assume that a person's utility over two goods is given by U(x1, x2) = (x1 - 5)^{1/3}(x2 - 10)^{2/3} The price of good x1 is equal to p1 and the price of good x2 is p2. The total income of the individual is given by I. (a) Write down the budget constrai
- Utility function from consuming a bundle of goods (X,Y) is given as and Prices are given as =($2, $4), and income M=$100 1. Derive the optimum consumption bundle. 2. If prices now change to =($4, $4).
- Consider an individual who spends all her income on Rice (R) and Chicken (C). Suppose the consumer maximizes the following utility function, U = U(R,C) subject to the following income constraint of
- Suppose a consumer's utility function is given by U(X, Y) = X*Y. Also, the consumer has $180 to spend, and the price of X, P_X = 4.50, and the price of Y, P_Y = 2. a) How much X and Y should the consumer purchase in order to maximize her utility? b) How
- An individual utility function is given by U(x,y) = x�y. This individual demand (optimal purchase) equation for x is a factor a of I/px: x* = a (I/px). In this specific case, factor a is equal to....
- Suppose a consumer's utility function is given by U(X, Y) = XY. Also, the consumer has $720 to spend. The price of X is PX = $9, and the price of Y is PY = $9. a. How much X and Y should the consumer purchase in order to maximize her utility? b. How much
- Suppose an individual has a preference represented by the utility function U(X_{1},X_{2} = X_{1} + lnX_{2}. The individual consumes two goods,X_{1} and X_{2} and faces the prices P_{1} and P_{2}. Con
- A consumer with income y= $120 obtains utility from two goods X & Y with prices PX =$20 and Py= $10. The consumers budget constraint is written is 20x + 10 y= 120 (or as a first degree polynomial y =
- Consider the utility function u(x, y) = 2 ln x + ln y. Initially, the prices are px = $2/unit and py = $1/unit. The consumer has an income of $18. Suppose the price of good x increases to px = $3/unit. What is the new optimal consumption bundle? Illustr
- Suppose that income is m = 102, and prices are a = 2 and b = 5. Consider the following utility function: u(a,b) = (a + 2)(b +1) (i) Find the utility-maximizing quantities of a and b. (ii) What is t
- Suppose an individual has a preference represented by the utility function U(X1, X2) = X1 + lnX2. The individual ocnsumes two goods, X1 and X2 and faces the prizes P1 and P2. Consumption is constraine
- Consider the utility function u(x, y) = 2 ln x + ln y. Initially, the prices are px = $2/unit and py = $1/unit. The consumer has an income of $18. Derive the consumer s optimal consumption bundle. Illustrate your answer with a graph.
- Andy's utility function for goods X and Y is linear and is given by U(X,Y) = 2X + 3Y. Based on this utility function, we can conclude that goods X and Y are for Andy. The price of X is $4, the price
- A consumers budget constraint identifies the different bundles of goods and services that can be purchased, given income and prices. A bundle of goods that is located inside the budget constraint: i.
- Given that the utility function for an individual is: and Income 72, the price of good one 4, and the price of good two 4, and the new price of good one = 77, What is the change in consumer surplus fo
- A utility function is U(x,y) = min(x,y^2). If the price of x is $25, the price of y is $10, and consumer chooses 5 units of y. How much is the consumer's income?
- 1. Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = ln x + 2 ln y (MUx = 1
- Suppose that the price of good x is $30 and the price of good y is $30 and a hypothetical consumer has $600 to spend per period on goods x and y. Sketch the consumer's budget constraints. Be sure to i
- Consider a consumer with utility function given by u(x_1, x_2) = x_1x_2 . (i) Find the demands for goods 1 and 2 when the consumer faces prices p_1 \enspace and \enspace p_2 , and income m . (i
- Graphing the BC. Suppose that an individual has a weekly income of $180 to spend on goods X and Y, which have prices of $2 and $6, respectively. Graph the budget constraint. Suppose that the price of
- Assume a consumer is currently purchasing a combination of goods, X and Y, that maximizes her utility given her budget constraint, i.e., MUx/MUy = PX/PY. Now assume that there is a decrease in the price of Y. In this case, to once again maximize her utili
- Consider the utility function u(x, y) = 2lnx + lny. Initially, the prices are p_x = $2/unit and p_y = $1/unit. The consumer has an income of $18. Illustrate answers with graphs. A. Derive the consumer's optimal consumption bundle. B. Now, suppose the pric
- Jane has a utility function u(x, y) = x^4y^5. The price of x is p_x, the price of y is p_y, and Jane's income is W. What is the expression of her consumption of y as a function of prices and income (her optimal consumption is determined by the tangency ru
- Assume that the unit price of good A is $2, and the unit price of good B is $5. If an individual has income of $30, which of the following consumption bundles of (good A, good B) is on the edge of the budget constraint? A) (5,5) B) (5,4) C) (6,4) D (6
- Suppose Vivian has a utility function U = X^(0.4)Y^(0.6), which X and Y are two goods. The prices for X and Y are $4 and $6, respectively. She has $100 in her pocket. a. Explain why Vivian's utility function is a special case of Cobb-Douglas function. b.
- 1. A consumer has monthly income of $100. His utility function is given as U(x_1, x_2) = x_1 x_2. The market prices of two commodities are p_1 = $5, p_2 = $10. Draw his budget line and indifference c
- Suppose Vanessa has a utility function U(X,Y) = X^0.2 Y^0.8 , which X and Y are two goods. The prices for X and Y are $8 and $2, respectively. She has $200 in her pocket. (1) Please explain why Vanes
- Suppose that the utility function is given as u(x) = 2ln(x_1) + 3ln(x_2). (Note: The preferences represented by this utility function is strictly convex and monotonic.) How much of commodity 1 (x_1) and commodity 2 (x_2) will the consumer purchase as a fu
- Solve for the amounts of goods x and y that a consumer with the following preferences and budget constraint demands. You must show your work and state any assumptions you make. Max(3+x)(5+y) s.t. 5x
- Suppose that a person's preferences can be described by the utility function U = ? L n q 2 where 0 is less than ? is less than 1 . They have income Y and face prices of p1 and p2. a).What is the
- The slope of the budget constraint is determined by the: a. relative price of the goods measured on the axis, b. relative price of the goods measured on the axis and the consumer's income, c. preferences of the consumer, d. Both b) and c) are correct.
- Suppose goods 1 and 2 are perfect complements. All consumers have utility function U(q1,q2) = min{q1,q2}. The sum of consumers' income is 100. Supply of the two goods is given by: S1(p1) = 2p1 and S2(
- Utility You are choosing between two goods, X and Y, and your marginal utility from each is show in the table below. your income is $14 and the prices of X and Y are $ 2 and $ 1 respectively. || Uni
- Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.
- Suppose a consumer has a utility function U(X, Y) = min{X, 2Y}. Suppose the consumer has $945 to spend (M = 945) and the price of good Y is 1 (P_Y = 1). Fill in the table below.
- 1. Consider the utility function u x_1x_2 = x_1x_2. Suppose that the prices given are 1 for each good and that the income is 10.
- Suppose that an individual consumes transportation (T) and all other goods (G). Assume that the price of G is pg, the price of transportation is pt, and Y is income. (a) If this consumer spends all of her income on transportation, how much could she buy?
- A rational consumer's utility function is, U=X0.5 E0.5, where, U represents utility, X represents all other goods and E represents Energy. The consumer's budget constraint is $200 and the prices of En
- Suppose a consumer's utility function is given by U(X,Y) = X*Y. Also the consumer has $288 to spend, and the price of X, Px=16, and the price of Y, Py=1. How much X and Y should the consumer purchase
- Consider a rational utility maximizing consumer who is choosing between two goods clothing (C) and food (F), where the total utilities of the two goods are independent so that total utility (U) = Util
- Consider a consumer allocating a budget of $ 100 between two goods, X and Y. The price of X is $ 10 per unit and the price of Y is $ 5 per unit. (a) In a diagram show how the consumer's budget constr
- Consider a consumer with utility function given by u(x_1, x_2) = x_1x_2. A) Find the demands for goods 1 and 2 when the consumer faces prices p_1 and p_2, and income m. B) Are goods 1 and 2 normal goo
- Assume that the budget constraint shown is for $600 of income with a price of food equal to $2 and a price of clothes equal to $4. With an indifference curve and budget constraint as shown, will a TANF grant of $200 have the same effect on food consumptio
- A consumer has the following utility function: U(x, y) =x(y+1), where x and y are quantities of two consumption goods whose prices are P_x and P_y, respectively. The consumer also has a budget of B. Therefore, the consumer's Lagrangian is x(y+1)+Lambda(B
- Let MU_A and MU_B stand for the marginal utility of goods A and B, respectively. Let P_A and P_B stand for the price of goods A and B, respectively. Assume that for a given consumer MU_A and MU_B are equal each other, and P_A is greater than P_B. In this
- Let MU_A and MU_B stand for the marginal utility of goods A and B, respectively. Let P_A and P_B stand for the price of goods A and B, respectively. Assume that for a given consumer MU_A and MU_B are equal to each other, and P_A is greater than P_B. In th
- A consumer's utility is defined by the function: u(x_1,x_2) = x_1^(1/3), x_2^(1/2). Assume prices of x_1 and x_2 are respectively defined by P_1 and P_2 and the consumer has W dollars in income. 1: F
- Hal has a quasi-linear utility function for Food and Stuff, U(F,S) = lnF + S. The price of F is "1" and the price of stuff is "Ps" and Hal's income is I. a. What is Hal's budget constraint? b. Show that Hals' demand for food depends only Ps and not his in
- Suppose a consumer's utility function is U(X, Y) = X + 2Y. The consumer has $8 to spend (M = 8). The price of good Y is P_Y = $2. What are the respective demands of good X when P_X = 1/4, 1/2, 2, and 4 dollars?
- 11. A consumer has $400 in income, the price of food is $1 and the price of Y is $1. Also, the consumer has $100 in SNAP benefits that can only be used for food. BCno S is her budget constraint with n
- Consider the Romer model of labor supply. Specifically, an individual who seeks to maximize U(consumption) + V(leisure) subject to the budget constraint: where P is the price of consumption, W is the
- A utility function is U(x, y) = min {x, y2}. If the price of x is $25, the price of y is $10, and consumer chooses 5 units of y. How much is the consumer's income?
- a) A consumer has utility given by U(x,y) = square root of xy subject to the budget constraint 100 = 4x + y. Find the bundle that maximizes utility. b) Suppose the original utility is now written as
- Consider a consumer that consumes two goods, x and z, with the following utility function. U = x^{0.125}z^{0.875} Suppose initial values for income and the prices of goods x and z are y = 100, P_x =5, and P_z = 15, respectively, then the price of good x f
- Consider a consumer who has the utility function u(x1, x2) = a ln(x) + B ln(y) where x1 and x2 and the quantities consumed of the two goods and a, B > 0. Suppose the consumer is constrained to spend l
- Examine the budget constraint for a consumer who has an income of $4. What is the price of paper? a. $2 each, b. $0.50 each, c. $4 each, d. $1.50 each.
- All there is are movies (m) and food (f). The price of movies is $10 while the price of food is $5. I have $145 to spend on these two goods. My preferences are described by the following utility function: u(m, f) = m + f + mf. Graph the budget constraint
- Consider a consumer who consumes two goods and has utility function u(x_1, x_2) = x_2 + \sqrt{x_1}. The price of good 2 is 1, the price of good 1 is p, and income is m. Show that a) both goods are n
- Priyesh's preferences for goods x and y is given by the utility function U = x2/3y1/3. His income is $192 and the price of good y is always $1. Suppose the price of x starts at $8 and then decrease
- A consumer's utility function is given by U(x,y)=(x-2)(x+y-2) where x and y are the quantities of two goods consumed. Find the bundle of these two goods that maximize this consumer's utility.
- A consumers utility is defined by the function, U(x1,x2) = x1^1/2 x2^1/2 Assume the prices of x1 and x2 are respectively defined by $5 and $10, and the consumer has 20 dollars in income. a. Find the c
- Assume a consumer's utility function is U = (q_1)^0.5+ 2(q_2)^0.5 and her total income is $90. The price of both good 1 and good 2 is $1. (a) What is the bundle that maximizes this consumer's utility
- Assume that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.8
- Suppose a consumer has 600 dirhams to spend on goods X and Y. the market prices for these goods are P_x = 10 and P_y = 40. A. Write the equation for the consumer budget line. B. Illustrate the consumer's opportunity set C. Show how the consumer's budget s
- A consumer has preferences for two goods, 1 and 2, which can be represented with the utility function u(x_1, x_2) = 4x_1 + 3x_2. A. If a consumer has a budget of 20 AZN while prices of goods 1 and 2 are 2 AZN and 4 AZN, respectively, calculate the bundle
- The following utility functions represent preferences of a consumer over goods x_1, x_2 (and x_3). Prices of these goods are denoted p_1, p_2 (and p_3). Consumer has income m. Derive the demand functi
- Suppose Ann consumes only X and Y and her utility is given by U(X, Y) = min (3X, 5Y). The price of X is , and the price of Y is . She has income I = $90 to spend on X and Y (a) Are good X and good Y
- Let MUa and Mub stand for the marginal utility of goods A and B, respectively. Let PA and PB stand for the price of goods A and B, respectively. Assume that for a given consumer MUa and Mub are equal to each other, and PA is greater than PB. In this case,
- Suppose an economy has two consumers, A and B, and two commodities X and Y. A's utility function and initial endowment are: U_A(X_A, Y_A) = X^{1/3}_A Y^{2/3}_A omega_A = (omega_{AX}, omega_{AY}) = (30
- A consumer's utility function is U(x; y) = (x + 2)(y + 1). The prices are p_x = $8; p_y = $2. The consumer consumes both goods. If his consumptions of good x is 14 units, what is his consumption of good y? Why?
- An individual has a budget constraint of $28. The price of healthcare is $2 and the price of all other goods is $4. a) Graph their budget constraint. b) Label the axes. In other words, indicate whethe
- An agent consumes goods x and y, with prices Px = $5 per unit and Py = $8 per unit. The consumer's income is I = $48. The government imposes a tax of $1 per unit on good x. What is the new equation for the budget constraint? a) y = 6 - (5/8)x b) y = 6 -
- A particular individual consumes two goods, X and Y. This consumer's marginal rate of substitution of X for Y is MRSXY=3QY/5QX The consumer's current income is $1,200, while the prices of X and Y are
- Suppose a consumer has a utility function given by U = 4X +12Y. The price of X is $2 and the price of Y is $1. The consumer has $24 (his income) to spend on the two goods. Plot good X on the X-axis and good Y on the Y-axis.
- Suppose the price of A is $20 per unit, the price of B is $10 per unit, the consumer's income is $1000 per month, and the consumer's budget line is BL1. Then the price of A goes down, price of B remains the same, the income goes up, and the new budget lin
- Suppose a person's utility function takes the Cobb-Douglas form U(C,R) = C^0.4 R^0.6, where C is consumption, and R is recreation. Assume that the price of the consumption good is 1 and that the consu
- Budget constraints impose scarcity, and are based upon a. How much utility one more unit of a good will provide b. The prices of the items purchased c. The limitation of the budget
- Suppose that the utility function is given U(x)=x_1^2 x_2^3. How much of commodity 1 (x_1) and commodity 2 (x2_) will the consumer purchase as a function of p_1, p_2, and m?
- Budget constraints impose scarcity and are based upon: a) the limitation of the budget. b) how much utility is one more unit of a goodwill provide. c) the prices of the items purchased.
- Consider three ways of allocating two goods in a two-person exchange economy. I. Both individuals take prices as given and equilibrium prices are established by an impartial auctioneer. II. One individual can act as a perfect price discriminator and force
- Given an individual utility function of the nature U(X1,X2 )= 1/4 \ln X_1+ 3/4 \ln X_2 a) Derive the consumers' indirect utility functions b) Derive the consumer's expenditure function c) State and