Consider the utility function: u(x1, X2) = Axfx}-a where 0 < a < 1, and A > 0. (a) Compute the Marshallian demand functions. (b) Derive the indirect utility function.
Q: 3. Consider the utility function: u (x1, x2) = In (1 + x1) + In (1 + x2) With the Marshallian demand…
A: We are going to take the support of Slutsky equation to answer this question.
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A: Given U = x2 + y2 + 2x + 2y Px = 1 Py =1 Income = 4
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A: Marshallian demand curve equations are attained by maximizing the utility with the budget(income) as…
Q: Derive the Slutsky equation from the starting point that: x(р,, р,, М) %3D х. (Р,, Ру, x. (P,, P,,…
A: Slutsky Equation is defined as the equation which shows the total change in demand consists of the…
Q: Consider a simple quasi-linear utility function of the form U(x, y) = x + In y. a. Calculate the…
A: Since you have posted a question with multiple sub-parts, we will solve the first 3 sub-parts for…
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Q: Suppose that an individual consumes two goods X and Y, and his direct utility function is given by:…
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Q: For the following utility function, u(x, y) =Vxy, (a) Verify that Shephard's Lemma:…
A: We are going to use marginal rate of substitution to find marshallian demand for both goods. Income…
Q: An agent consumes quantity (x1,x2) of goods 1 and 2. Here is his utility function: U(x1, x2) =…
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Q: ider the indirect utility function: V(P;» P2, m) = (m + p,+ p,)} - 4p;P, 2 4p;P2 Derive the…
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Q: A consumer is faced with the followlling Utility Function, U(x, x2) = (x 1+ x ) e, where 0<p<1. The…
A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…
Q: Derive demand functions for x and y for the general class of Cobb-Douglas preferences represented by…
A: The utility function of Cobb-Douglas preferences is given as,
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Q: Let a consumer's preferences are reflected by a Cobb-Douglas utility function i.e., UXLX) = Xf x5 BM…
A: X1= αMP1 Question1: Price elasticity of good X1: = dX1dP1*P1X1 =-αMP12 * P1X1= -αMP1(αMP1) = -1…
Q: M (II) Consider indirect utility function U* = (- a + B' a+/ (a) Find Marshallian demand functions…
A: Indirect utility function (IUF) shows the relationship between price of goods and income of the…
Q: True or false? If the demand function is x1 = −p1, then the inverse demand function is x = −1/p1.
A: Inverse demand function states that price is a function of quantity where the demand function states…
Q: Given the utility function: U = X3/4 .Y1/4 Estimate the demand functions of commodity X and…
A: Given U = X3/4 .Y1/4 Price of X = PX Price of Y = PY Income = M We know that Budget line Equation…
Q: Consider the following strictly quasi-concave utility function u(q1, 92) = J91 +2/q2 Assume that…
A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…
Q: Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is…
A: (1) u = 8x0.5 +y Differentiate u w.r.t x to get marginal utility of x =>MUx = du / dx => MUx…
Q: An agent consumes quantity (x1,x2) of goods 1 and 2. Here is his utility function: U(x1, x2) = x13…
A: Utility function is x13x2 with budget constraint p1x1+p2x2=m At optimum, MUX1MUX2=p1p2
Q: assume that both X and Y are goods s.) Consider a person whose preferences can be represented by the…
A: We first define the properties of each type of good in terms of price elasticity as well as income…
Q: A consumer has Hicksian demand functions h(p1 p2, u)=a()*"ū and h(p1 P2, u)=(1 a)()"ū. Determine…
A: In this question we have to find the Marshallian demand function and slutskey's Equation.
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Q: Suppose the utility function for goods x and y is given by utility = U(x, y) = xy + y. a. Calculate…
A: Answer a) Uncompensated demand Function for the two goods. Utility Function U(x,y) = xy + y Budget…
Q: Given the utility function Log Y = 0.42logX1 + 0.58logX2 Find the demand function
A: Given Utility function logY=0.42logX1+0.58logX2 .... (1) Let the price of good 1 and good 2…
Q: Assume that utility is given by and Income I, price of good x = P = U(2,y) = 03J0.7 and price of…
A: Given Utility function: U(x,y) =x0.3y0.7 ..... (1) Income =I Price of x = px Price…
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A: Utility function : U(x1 , x2 ) = (xp1 1+xp2)1/p Budget Constraint : p1x1 + p2x2 = m Firstly we…
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Q: Assume you spend your entire income on two goods X & Y with prices given as Px & Py, respectively.…
A: Utility function, U = X2 + Y2Price of good X = PxPrice of good Y = PySo, XPx + YPy = I…
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Q: Let u(x.y)=(x+2)y. Find the following a. the Marshallian demand functions for x and y b. the…
A: We have a utility function u(x,y)=(x+2)y .... (1) Let the price of good x is px and the…
Q: Consider the following utility function U(x1, x2) = Min{x1, x2} + 1/2Max{x1, x2} Calculate the…
A: U(x1,x2) = Min{x1, x2} + 1/2Max{x1,x2}
Q: Assume you spend your entire income on two goods X & Y with prices given as Px & Py. respectively.…
A: Given that Marshallian demand function U = X2+Y2. Price of good X = Px and price of good Y = Py
Q: Q2 Consider the Cobb-Douglas utility function, u,(X, Y) = Xª Y' -ª for a rational consumer i. Derive…
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Q: Consider a simple, quasi-linear utility function: U(x,y) = x + ln y 1. Derive the uncompensated…
A: Given, Utility function: U(x,y) = x + ln y 1. To derive uncompensated (Marshallian) demand function,…
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A: Since you have posted multiple questions, we will answer the first question for you. If you want any…
Q: Given the utility function and budget constraint z = 3X, +X;X; +2x: M= P,X, + P:X; Obtain…
A: Part a) Given : z = 3X1 + X1X2 + 2X2 M = P1X1 + P2X2
Q: Assume you spend your entire income on two goods X & Ywith prices given as Px & Py, respectively.…
A: Marshallian demand Function U = X2 + Y2 Budget line = Px+Py = m For Optimal Bundle MRSxy = Slope of…
Q: 3. Consider the following quasi-linear utility function U(x, y)=x+In y. Find the uncompensated…
A: Utility function: U(x,y) = x + ln y
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A: (Q)Suppose a consumer’s utility from consuming the two goods x and y is given by: U(x,y)= x +…
Q: Consider the following Utility Function 1 3 U = q; q a) Derive the Hicksian demand functions. b)…
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- Praxilla, who lived in ancient Greece, derives utility from reading poems and from eating cucumbers. Praxilla gets 30 units of marginal utility from her first poem 27 units of marginal utility from her second poem 24 units of marginal utility from her third poem, and so on, with marginal utility declining by three units for each additional poem. Praxilla gets six units of marginal utility for each of her next three cucumbers consumed, five units of marginal utility for each of her next three cucumbers consumed, four units of marginal utility for each of the following three cucumbers consumed, and so on, with marginal utility declining by one for every three cucumber consumed. A poem costs three bronze coins hut a cucumber costs only one bronze coin. Praxilla has 18 bronze coins. Sketch Praxillas budget set between poems and cucumbers, placing poems on the vertical axis and cucumbers on the horizontal axis. Start off with the choice of zero poems and 18 cucumbers, and calculate the changes in marginal utility of moving along the budget line to the next choice of one poem and 15 cucumbers. Using this step-by-step process based on marginal utility, create a table and identify Praxillas utility—maximizing choice. Compare the marginal utility of the two goods and the relative prices at the optimal choice to see if the expected relationship holds. Hint: Label the table columns: 1) Choice, 2} Marginal Gain from More Poems, 3) Marginal Loss from Fewer Cucumbers, 4) Overall Gain or Loss, 5) Is the previous choice Optimal? Label the table rows: 1) 0 Poems and 18 Cucumbers, 2) 1 Poem and 15 cucumbers, 3) 2 Poems and 12 cucumbers, 4) 3 Poems and 9 Cucumbers, 5) 4 Poems and 6 cucumbers 6) 5 Poems and 3 Cucumbers, 7) 6 Poems and 0 Cucumbers.For normal goodsA) the substitution effect of a price decrease will decrease the quantity of the good demanded while theincome effect of a price decrease will increase the quantity of the good demanded.B) the substitution and income effects of a price decrease will both increase the quantity of the gooddemanded.C) the substitution and income effects of a price decrease will both decrease the quantity of the gooddemanded.D) the substitution effect of a price decrease will increase the quantity of the good demanded while theincome effect of a price decrease will decrease the quantity of the good demanded.Assume that a consumer consumes two diff erent goods, and the utility function is u(x)= u (x1, x2) = x1x2, the production function of t wo goods is y=1/2+(x-5/8)1/3 at first, then t he function of goods 1 changes to y=1/2+(x -325/8)1/3. Assume that her income is M = 1 8. Calculate the compensating variation and equivalent variation. A B EV-15-6√3 CV=16√3-15 C CV=16√3-15 EV-15-6√3 D EV 18√3-18 CV-18-6√3 EV-18-6√3 CV-18√3-18
- Law of equi marginal utility is an important law of cardinal utility analysis. Explain this law with the help of its assumptions. Also explain the mechanism that how the total utility will be maximum at a point when the marginal utilities of both the goods become equal. Furthermore, there is a relationship between total and marginal utilities where they both pass through different stages when the consumer continues his or her consumption regularly. Describe this case brieflyExplain the difference between a positive and a negative network externality. A network externality for a good is positive if O A. the substitution effect of a price change is larger than the income effect, but a network externality is negative if the income effect is larger than the substitution effect. B. consumption by others decreases a typical consumer's marginal utility from consuming the good, but a network extemality is negative if consumption by others increases a typical consumer's marginal utility from the good. c. the price is lower the more people own it, but a network externality is negative if the price is lower the fewer people own it. D. the quantity demanded is higher the more people own it, but a network externality is negative if the quantity demanded is lower the more people own it. O E. it has a complement, but a network effect is negative if it has a substitute. Give an example of each. An example of a positive network externality is the dermand for A. a work of…I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?
- Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.7 Asen tries to minimize his cost of using two goods x subscript 1 end subscript and x subscript 2 end subscript. The price of the first good is BGN 12 and the second good BGN 8. His utility function is x subscript 1 superscript 3 divided by 5 end superscript x subscript 2 superscript 2 divided by 5 end superscript and the utility he will get from using both goods, is 32 units. Find the Hicks quantities demanded and what Assen's minimum budget must be to consume these quantities and obtain the above utility. e-412, h2=21, h1=21 e=416, h2=21, h1=21 e=640, h1=32, h2=32 e=422, h2=21, h1=21 e=378, h2=21, h1=21 e-378, h2=20, h1=20 another answer e-378, h2=24, h1=24
- Which among the following is not true?Select one:a. None of the answers are correctb. When marginal utility declines, a higher price is needed to induce the consumer tobuy more of a particular productc. When marginal utility declines, a lower price is needed to induce the consumer tobuy more of a particular productd. All the answers are correcte. Utility maximizing rule and the demand curve are logically consistentPls help with thsi question I am stuck Given the image attatched: 1.Given the above Marginal Utilities and prices to form the optimality condition for utilitymaximization. According to this optimality condition, what must be the ratio of Films toBooks in an optimal consumption bundle? 2. Given your answer to Q9, what must be the household’s optimal consumption of F & Bgiven their income (m)? 3. Suppose that the price of Films changed from $2 to $4. What would need to happen tothe MRS according to the optimality condition in Q9 if the household wanted to keepmaximizing its utility?As more of a good is consumed in a given period, its... total utility remains constant total utility decreases then increases O marginal utility decreases O marginal utility increases
