In a 2-good model, where the goods are denoted X, and x2, the consumer's utility 1 1 function is as follows: U = x Money income available is denoted m. All of this income is spent on the two goods. The prices of the two goods are p1 and p2 respectively. By minimising expenditure, subject to the utility function, find the compensated (Hicksian) demand functions; that is, demand for each good expressed in terms of U, p, and pɔ. Do not check the second order conditions.
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Can you please help solve question 8 I have added a similar question AWNSERED so it is easier to understand the logic behind it, please show full working so I can compare it to my own work I am having trouble with the algebra
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- Draw the compensated (hicksian) and uncompensated (marshallian) demand curves when: a) both normal goods when price of good 1 increases b) both normal goods when price of good 1 decreases c) both inferior goods when price of good 1 increases d) both inferior goods when price of good 1 decreases e) one normal good, another inferior good when price of inferior good (good 1) increases f) one normal good, another inferior good when price of inferior good (good 1) decreasesQuestion 3 Consider the utility function of the form: ?=?1?1?2?2 Given the budget constraint: ?1?1+?2?2=? Show that the implied Marshallian demand curves are: ?1=?1(?1+?2)??1 ?1=?2(?1+?2)??2Consider the following function describing the utility of a consumer: U(x1, x2, x3) = a1*ln(x1) + a2*ln(x2) + a3*ln(x3), where ln = natural logarithm and a1, a2, a3 constants a. Pose the primal problem (using Langrange's method), obtaining the Marshallian demands for each good and the individual's indirect utility function. b. From the results obtained from question a., find the minimum expenditure function and the Hicksian demands.
- Suppose U = 2X + Y, I = 20, Px = 2, and Py = 2. (a) Find Marshallian demand for X and Y . (b) What is Marshallian demand for X and Y if the price of X increases to 5? How much of the change in demand for X is the income effect and how much is the substitution effect? (c) How much is compensating variation for the price change described in part (b)? (d) How much is equivalent variation for the price change described in part (b)? ( Please solve all the subparts ASAP I will give you thumbs up . )The consumer has an incom Mand a utility function of the form u (x1; x2) = aInx1 + (1 - a)Inx2 If the prices of the two goods are given by p1 and p2, derive the Hicksian demand functions for a given utility level U: Derive the expenditure function. Using the concept of duality, derive the indirect utility function.Suppose that X is an inferior good. A. Show using well labeled diagrams how you would derive the Marshallian Demand curve and compensated demand curve holding utility constant for a consumer maximizing her welfare subject to a budget constraint. B. Derive the consumer's compensated demand curve and draw the demand curve carefully for X, Under the two following rules to measure the amount of compensation required to estimate the substitution and income effects. (1) holding real income constant. (2) holding production possibilities constant (assume linear). C. Under what real model circumstance would you employ these scenario for measuring the compensated demand function for a good?
- Answer both question (a) and (b) below. (a) State theWeak Axiom of Revealed Preference (WARP). (b) In a two-good model, suppose a consumer always chooses the midpoint of the budget line given any (p1; p2; I), does the demand function satisfy WARP? Why? (HINT: Graphs can be helpful to answer the question.)Consider a consumer with utility function u(x1, x2) = α_1x_1^( 2) + α_2x_2^( 2) where α1 > 0 and α2 > 0. Assume that p1, p2 > 0.? (a) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (b) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utilityThe utility function of a certain consumer is U =(x1,x2)= x11/3 x22/3 , x 1and x 2 is the consumption of two kinds of goods, and the consumer's income is 100. The current prices of the two kinds of goods are P 1 =1 and P 2=2 respectively, ask: 1. If the price of the first commodity increases from 1 to 2, and other factors remain unchanged, what is the total effect of the price increase on the consumption of the first commodity? According to the Slutsky decomposition principle, what are the income effect and substitution effect? 2. Calculate the amount of income compensation that changes the price of the first commodity from 1 to 2, keeping the original effect unchanged
- Assume that utility is given by u(x, y) = x0.3y0.7 1. Derive the Walrasian demand function. Then use the derived Walrasian de- mand functions to compute the indirect utility function. 2. Derive the expenditure function and the Hicksian (compensated) demand functions for this case. Hint: Use Propositions 5 and 4.Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.It is an established fact in economics that for goods which are described as inferior goods, when incomes of consumers increase, consumers tend to reduce their consumption of such goods and rather patronize goods which would normally provide higher satisfaction .If a researcher decides to undertake a study to verify the general preposition that as incomes rise, the consumption of inferior goods falls, which type of economic study and what analysis is this? Justify your answer.