# Suppose that you know the utility function for an individual is given by the equation U= XY where...

## Question:

Suppose that you know the utility function for an individual is given by the equation U= XY where U is the total amount of utility the in and good Y. You are also told that this individual's income is $100 and that the price of good X is $2 and the price of good Y is $4. From this information answer the following set of questions.

(a) What is the consumption bundle of good X and good Y that maximizes this individual's utility given their income, prices of the two goods, and their tastes and preferences as measured by their utility function? Support your answer with a well labelled diagram Hint: e.g. Mux = dU/dX) (b) What is the level of utility this individual gets when they maximize their utility given the above information? (c) Suppose that the price of good X increases to $4 and nothing else changes. What is the new consumption bundle that maximizes the individual's utility no the price of good X has increased? What has happened to his utility? Determine the SE and IE .

## utility Maximization:

Utility maximization refers to the objective of a rational consumer to derive the maximum possible satisfaction from the consumption of a bundle of goods under the constraint of a budget defined by the income of the consumer.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answerUtility Function:

{eq}U = XY {/eq}

Budget Constraint:

{eq}$100 = 2X + 4Y {/eq}

**Ans. (a)**

The utility is maximized at the point where the...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 3 / Lesson 2Learn about utility maximization. Discover various types of utility, examine utility maximizing rules, and study examples of maximizing utilities in economics.

#### Related to this Question

- Suppose that you know the utility function for an individual is given by the equation U = XY where U is the total amount of utility the individual gets when they consume good X and good Y. You are also told that this individual's income is $100 and that t
- Suppose that the utility function of an individual can be described as U(X, Y) = X + Y. For this utility function the MRS A) is always XY. B) is always X - Y. C) is always X/Y. D) is always X + Y. E) is always constant.
- Suppose that individual A's utility function, which only depends on wealth, is defined as U(W)= W^(1/2), where W stands for wealth. a. What is his level of utility when W= 1000;
- Suppose a person has a utility function U=YX. What is the minimum level of income required to get a utility of 20? Your answer should be a function of, among other things, Px and Py.
- In a two good world, a consumer has the indirect utility function. V(p,w)= w/2(p1)^(-1/2)p2^(-1/2) After determining the necessary function, verify the Slutsky equation holds for the first good invo
- For the following function: U= \left (\frac{x_1 x_2}{ x_1^2} \right)x_2 a. Determine mathematically whether the utility function given above is homogeneous, b. Determine and explain the degree of homogeneity for the utility function if it is homogene
- Suppose consumption is a linear function of disposable income: C(Y-T) = a+b(Y-T) where a is greater than 0 and 0 is less than b is less than I. Suppose also that investment is a linear function of the
- Calculate the expected utility of income? (expected value of utility of income) Utility function is U = Y^{0.5}
- Suppose you are given the following consumption and income data: |Consumption |100 |190| 280| 370 |460 |550 |Income| 0 |100 |200 |300| 400 |500 Obtain an equation for the consumption function. Use your function to predict the value of consumption wh
- Assume that the level of autonomous consumption in Mudville is $400. If the marginal propensity to consume is 0.9, what is the consumption function? The saving function? Give an equation for each and show each graphically. At what level of income is savin
- Consider the following utility function: U(X, \: Y) = 10X^{0.5} + 5Y. Find the marginal utility of each good.
- An individual utility function is given by U(x,y) = xy. Derive this individual indirect utility function. Using this individual indirect utility function, compute her level of utility when I = $800,
- Use the table above to answer the following question. Suppose the person's utility function is given by U = I0.5, where I is income. What is the person's expected utility? A) 270 B) 45 C) 184 D) 81
- Suppose we calculate MRS at a particular bundle for a consumer whose utility function is U(q_1,q_2). If we use a positive monotonic transformation, F, to obtain a new utility function, V(q_1,q_2) = F(
- Consider the following utility function (referred as a quasi-linear utility function as it is linear in the second element): u(x,y)=ln(x)+y. with prices and income given by: p_x=1,p_y epsilon R_+ and
- Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I and is concave (in other words, our basic assumptions). Let IS = 200 be this person's income if
- A consumer has the utility function f(x_1,x_2)=20x^{\frac{1}{3_1 x^{\frac{1}{4_2. The difference curve on which utility is 40^{\frac{2}{4} has the equation a. x_2=0.16x_1^{-\frac{4}{3 b. x_2=0.01x_1^{-\frac{4}{3 c. x_2=0.25 x_1^{\frac{3}{4 d.
- Suppose the consumption function is C=127+0.79YD. If disposable income is $400, consumption is what?
- Suppose that an individual has a utility function U(c) = c 1=2 : They have 400 dollars. With probability 0.1 they get sick, which results in complete loss of their wealth (their wealth becomes 0). Wh
- Harry's budget constraint is given by PX+PyY=60, and P=$5, Py=$2. Suppose Harry's utility function is given by the equation U XY, where U is the level of utility measured in utils and X and Y refer to
- Suppose you have a two-good world, good X and good Y, and a utility function U=xy. On a graph, draw the indifference curve for total utility equal to 100.
- Consider the utility function U=x^a+ay a=alpha I=Pxx+Pyy (a) What is the optimal combination of x and y? (b) Solve for the indirect utility function. (c) Show that utility is increasing in I and de
- Advanced Analysis Suppose that the linear equation for consumption in a hypothetical economy is C = 40 + 0.75Y Also suppose that income (Y) is $400. Determine the following values. a. MPC b. MP
- Consider the following utility function: U(X, \: Y) = 10X^{0.5} + 5Y. Derive the equation for the indifference curve, where utility is equal to a value of 100.
- Suppose that Sally's preferences over baskets containing petrol (good ''x'') and food (good ''y'') are described by the utility function U(x,y)=xy+100y . The marginal utilities for this function are,
- Consider the following utility function, utility = x�y. The equation for the indifference curve at utility level equal to 20 is: (Choose one and show your work.) a. 100 = xy b. y = \frac {100}{x} c.
- Consider the utility function U= (x-theta)^a(y-p)^(1-a) a) Provide an intuitive explanation for this kind of preference; that is, what roles do a and p play? b) Solve for the optimal combination of x
- Assume that Sally has the following utility function: U = B2 + 4Z2. Sally's income is $200, PB equals 1 and PZ equals 4. Determine the quantity demanded of Z. Show all of your work. (Hint: draw a coup
- Suppose that Sally's preferences over baskets containing milk (good x), and coffee (good y), are described by the utility function U(x, y) = xy + 2x. Sally's corresponding marginal utilities are, MU_x
- How do I solve this "Tom spends all his $100 weekly income on two goods, X and Y. His utility function is given by U(X,Y) XY. If PX = 4 and PY = 10, how much of each good should he buy?"
- An individual utility function is given by U(x,y) = x�y. I = $800. px = $20, py = $40. The value of the Lagrange multiplier ? associated with the utility maximizing income allocation is ..... . (NOTE:
- Suppose your utility function is U=ln(4I) where I is the amount of income you make in a year. Suppose that you typically make $30000 per year, but there is a 5 percent chance that, in the next year,
- For the following utility function: U=(x1x2/x1^2)x2. a. Determine whether the utility function given above is homogeneous. b. Determine the degree of homogeneity for the utility function, if it is hom
- Given an income equation: $150 = ($10 x Juice) + ($5 x Bread) and the utility function: (U = J.75 B.25) a.1.) First, calculate the indifference curve at the optimal levels of consumption of J and B. W
- Given the following utility function: U = (2x_(1)x_(2) + 3x_(1)^(2))^(3)x_(2) a) Find the marginal utility for x_(1) and x_(2). Do not simplify the function. Work with it in the form given. b) Show m
- Suppose your utility function for income that takes the form U(I)=SQRT(I) (i.e. square root of income), and you are considering a self-employment opportunity that may pay $10,000 per year or $40,000 per year with equal probabilities. What certain income w
- Suppose that the linear equation for consumption in a hypothetical economy is: C = 40 + 0.75Y Also suppose that income (Y) is $400. Determine the following values: For parts a, b, d, and f, round your
- Suppose that an individual consumes three goods: food, clothing and automobiles. Denote the quantities of these goods consumed by X, Y, and Z respectively. Suppose the individual utility function is given by: U = 5 ln x + 4 ln y = ln (1 + z) and the pric
- Assume a person with Cobb-Douglas utility U = q_1^{.6} q_3^{.4} currently pays $15 for each unit of good #1 and $20 for each unit of good #2. Income is $1,000. Solve for the equivalent variation (EV
- Kyle's utility function is U(x,y)=(x+2)(y+1), where x is consumption of good x and y is the consumption of good y. a) Write an equation of an indifference curve going through the point (x,y)=(2,8), b) Graph the indifference curve with U=36 in the x-y sp
- Imagine that the indirect utility function of an individual is given by V(p_x, p_y, I) Imagine that the indirect utility function of an individual is given by V (P_x; P_y; I) = 1^2/ 4p_xp_y . Find the
- Phil's utility function is U = XY , where MU_ X = Y and MU _Y = X . In Lancaster, Pennsylvania, Phil's income would equal $500, and the prices of good X and good Y are $5 and $5, respectively. In Washington, D.C., Phil's income would equal $800, and the p
- Consider the utility function U = X^a + ay, where a = alpha. A) What is the optimal combination of x and y? B) Solve for the indirect utility function. C) Show that utility is increasing in I and decr
- Consider the utility function: U(x, y) = (A*x^p + B*y^p)^(1/p). Derive the MRS.
- Suppose the marginal propensity to consume fell to .75, autonomous consumption fell by 100, so that equation of consumption function became C =.75Y + 200.
- Suppose Theon has a utility function of the form U=C11/3C22/3 and has an income of $100 today and $0 tomorrow. Find Theon's supply of savings function.
- Consider the following utility function: U(X, \: Y) = 5X + 2Y. Derive the equation for the indifference curve where utility is equal to a value of 100.
- Consider an economy that is described by the following equations: C = 140 + 0.80(Y - T) - 200r Consumption Function T = 400 + 0.1Y Tax Function I = 1000 - 700r Investment Function L = 0.5Y - 1000i
- If the utility function for the consumer is: U = min{10 x1, 50 x2} P1= 4 , P2=6 and I=2,000, what is the level of maximized utility?
- A) Suppose an individual has preferences over two goods that can be represented by the utility function of u(x,y) = x^(1/2) y^(1/2), where 'x' and 'y' represent the quantities consumed of each good. C
- Consider the utility function: U(x, y) = (A*x^p + B*y^p)^(1/p). Derive the MU_y.
- Consider the Utility function: U(x, y) = -1/x - 1/y. Derive the MRS.
- Suppose that the consumer's preferences are described by the utility function U(x; y) = 5x + y, where y denotes the quantity of good Y and x denotes the quantity of good X that the consumer consumes. Suppose also that the consumer's income is 600 euros, t
- Consider the following utility function: U(X, \: Y) = X^{0.33}Y^{0.67}. Derive the equation for the indifference curve, where utility is equal to a value of 100.
- Suppose a consumer has references re resented by the utility function U(X, Y) = MIN[X, 3Y]. Suppose P_x = 2 and P_y = 4. Draw the Income Consumption Curve for this consumer for income values M = 100, M = 200, and M = 300. Graph should accurately draw the
- Consumption the multiplier: how to derive an IS curve that includes and show the consumption multiplier. That is, show how to derive equation below. Draw a graph of the original IS curve that includes
- Suppose there are two consumers, A and B. The utility functions of each consumer are given by: U_(A) (x, y) = xy^(3) U_(B) (x, y) = xy Therefore: For consumer A: MU_(x) = y^(3); MU_(y) = 3xy^(2) Fo
- An individual utility function is given by U(x,y) = x�y. I = $800. p_x = $20, p_y = $40. At the point at which this individual maximizes her utility level she buys _ unit(s) of x and _ unit(s) o
- Refer to the table below. The value of X is: a. 5 b. 10 c. 15 d. 55 Units Consumed Total Utility Marginal Utility 0 0 - 1 W 20 2 35 X 3 Y 10 4 40 Z
- Suppose that Colin's preferences for goods X and Y can be represented by the utility function U(x,y) = min[x,y], where x (respectively, y) is the amount of X (respectively, Y) that he consumes. min[x,
- Assume that an individual has the following utility function U(C1, C2) = 4C1+2C2. For this utility function, which of the following is true about MRS1,2? A.) It depends on the values of C1 and C2 B.) It is always 0.5 C.) It is always 2 D.) It is alway
- Suppose that the linear equation consumption in a hypothetical economy is: C = 50 + 0.75Y Also suppose that income (Y) is $500. Determine the following values: a. MPC = b. MPS =c. Consumption = d. AP
- Show that if a utility function u(x) is homogenous of any degree k, then the indifference curves have the same slope along any ray through the origin in the consumption set. Interpret the economics of
- Suppose a consumer's utility function is given by U = (q_1,\; q_2,\; ...,\; q_n). Derive Engel's Aggregation Condition.
- 1. If utility is given by u(x,y)= square root of {xy}, then the person's MRS at the point x = 5, y = 2 is given by a. 1.0 b. 3.5 c.0.4 d. 5.0 2. "If an individual is to maximize the utility received f
- Suppose that Sally's preferences over baskets containing coffee (good x), and milk (good \sqrt{y}), are described by the utility function U(x,y) = 40 x+y. Sally's corresponding marginal utilities are,
- Assume that an individual's preferences is represented by the utility function U(x, y) = 5x + 2y. A. What could you tell about the type of x and y? Good, bad, or neutral? B. Derive the equation for his/her indifference curve for utility level of 100. C. D
- Sherlock has a utility function of U = XY, where X is the quantity of good X and Y is the quantity of good Y. Sherlock's marginal utility of good X, MUX=Y and Sherlock's MUY = X. a. What is an equati
- A consumer has the utility function U(x,y) = x^{\alpha} y^{\beta}, where x is greater or equal than 0 and y is greater or equal than 0 represent her consumption of goods X and Y, and \alpha is greater
- Consider the utility function U(x, y) = xy. a. Is the assumption that "more is better" satisfied for both goods? b. What is the MRSx, y for this utility function? c. Is the MRSx, y diminishing, con
- How do we find the expenditure function, when we get a certain utility function?
- Consider the utility function U (q1, q2) = 4q1^{1/2} q2^{1/2} + q2 that describes Bob's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. a) Derive an expression for his marginal utility (U1) from a small
- Show that the following utility function is homogeneous of degree 1 in quantities demanded of x and y: U (x, y) = x^2*y^8 B) Show that the following utility function is homogeneous of degree 2 in quan
- Consider a class of utility functions which are "additively separable," i.e., a. Find the first and second order conditions for utility maximization for these utility functions. Show that diminishing
- If the proportion of disposable income that is saved equals 0.80, what is the slope of the consumption function?
- Compute the expenditure function from the Cobb-Douglas utility function and quasi linear utility function with steps.
- Consider the following utility function. A. What is the name for a utility function of this form? (a) Negative exponential. (b) Fixed proportion. (c) Perfect substitutes. (d) Cobb-Douglas. B. Fix a u
- Consider the following model: C=20+0.5(Y-T) I=20-10r T=0 G=50 a) Obtain the equation of the IS curve. What is the slope of the curve? Calculate output if r=0.1 b) Suppose now that autonomous con
- Jenna's utility is represented by U(X,Y)=XY. If she had 6 of each, then her utility is XY = 36. a. Solve for the Y as a function of X that is needed to maintain this level of utility, U = 36. b. Der
- Marcia's utility function is U= 30P^{0.7} W^{0.3} where P is pasta, and W is wine. The marginal utility of pasta is MU_P=21P-0.3 W^{0.3} and the marginal utility of wine is MUW=9P^{0.7} W^{-0.7}. a.
- Consider the following utility functions: 1. u(x1,x2) = x1 + 2x2 2. u(x1,x2) = 2x1^{0.25} x2^{0.75} 3. u(x1,x2) = 1/2x1^2 - x2 4. u(x1,x2) = min{x1,2x2} 5. u(x1,x2) = max{x1,2x2} Give the equation of
- Brad consumes good x_1 and y_1 and has a utility function of the form u(x_1,y_1) = x_1 + y_1 and an initial endowment x_bar_1=6 and y_bar_1=12. Angelina consumes goods x_2 and y_2 and has a utility f
- When graphing the consumption function, there will be a line called the 89-degree reference line that will help us easily determine where real disposable income equals planned real consumption (that is, where the consumption function intersects that line)
- Suppose that a person has a utility of a wealth function given by u(w) = square root of w. Further suppose that this person's initial level of wealth is 100. A. Suppose that this person faces a possible
- A consumer has the utility function U(x,y) = x^alpha y^beta, where x is greater than or equal to 0 and y is greater than or equal to 0 represent her consumption of goods X and Y, and alpha 0 and bet
- Suppose Natasha's utility function is given by U=I^(0.5), where I denotes income. a. Is Natasha risk loving, risk neutral, or risk averse? Explain using calculus. b. Suppose that Natasha is currently
- Assume a consumer's utility function for goods x_1 and x_2 is of the following form: U(x_1,x_2) = x_1^2/3 x_2^1/3 Next, assume p_1 = 1, p_2 = 1, and Y = 120. a. Find the expressions for the consumer's
- Explain each part of a linear consumption function, including its intercept and its slope. Distinguish between autonomous consumption & induced consumption. How does the consumption function illustrat
- Suppose that Patrick has a utility function of the form of U = Min(alpha x, beta y). Patrick has an income of $100 and currently faces prices of Px = $1.00 and Py = $2.00. Suppose that the price of X
- Suppose the utility function for two goods, Tacos (T) and Nachos (N), has the Cobb-Douglas form U(T, N) = sqrt{TN}. Consider a logarithmic transformation of this utility function U'. What is the MRS of U'? A. frac{1}{2}frac{N}{T} B. frac{N}{T} C. frac{T}{
- Consider the following economy: C_a = 1800 ; c = 0.8 ; T = 1200 + 0.20 Y; I_P = 1800 ; G = 2000; NX = 600 - 0.08 Y. a) What is the value of the autonomous Tax T_a? b) Compute the value of the multiplier, c) Derive the equation of the autonomous spend
- Suppose an individual's preferences for two goods X and Y are characterized by the utility function: U(X,Y ) = X^{0.5} Y^{ 2} The marginal utility functions are given as: MU_{X} = 0.5X^{-0.5}Y^{2} a
- Suppose the consumer's utility is u(x, y) = 2x + 3y. The consumer's utility maximization problem is given by max (x,y) 2x + 3y s.t. pxX + pyY= i. Solve using the substitution method.
- There are 2,000 consumers with identical preferences for a good that can be summarized by quadratic quasi-linear utility function (u{x1, x2} = -(X1)2+ 10(x1) + x2 which implies MRS = 2(x1) -10). Assu
- Use the following to answer the questions: Units Consumed Total Utility Marginal Utility 0 0 1 W 20 2 35 X 3 Y 10 4 40 Z What is the value for X Y W and Z
- Consider the following individual utility functions and answer the questions.
- Assume that the consumption function is given by C = 200 + 0.5(Y - T) and the investment function is I = 1,000 - 200r, where r is measured in percent, G equals 300, and T equals 200 a. What is the nu
- Suppose the utility function for two goods Tacos (T) and Nachos (N), has the Cobb-Douglas form U(T, N) = \sqrt{T * N} A. Graph an indifference curve associated with this utility function B. Find th
- 1) A consumer has preferences for apples (A) and Oranges (Or) given by the utility function U(A,Or) = log(A) / 2 + log(Or) where log() is the natural logarithm function. The Marginal Utility for A is
- If the utility function is: U=99x1 + 93x2 How many units of x1 is the consumer willing to give up to get one more unit of x2?