Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y 2 , derive the Hicksian demand function for good Y.
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Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y 2 , derive the Hicksian
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- Consider an individual with the following utility function: Derive step-by-step both corresponding Hicksian demand functions depending on the different prices (P₁, P2) and a fixed utility level u. The equation given In picture.do This in 10 minutes.Consider the indirect utility function: v(p1; p2; m) = m /(p1 + p2). What is the Hicksian demand function?A consumer is faced with the following utility function, U(x1 x2)=(xp1 1+xp2)1/p, where 0<p<1. The consumer also faces the prices p1 and p2 and has income level m. C) derive the the corresponding expenditure function for the consumer and the hicksian demand function.
- It is given that a typical consumer has a well-behaved preference structure for his consumption bundle, which includes only two goods, A and B. Further, assume that commodity A is normal and commodity B is Giffen. By keeping commodity A on the x-axis and commodity B on the y-axis, you are required to show the price decomposition for commodity B when $PB decreases exogenously relative to $PA.Consider 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.A consumer has the following indirect utility function: u (x1, x2) = − 1/ x1 − 1 /x2 1. Compute the Walrasian demand functions.2. Obtain the indirect utility function.3. Obtain the expenditure function and the Hicksian demands.
- 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 the following indirect utility function:ʋ(P,y) = y(P1r + P2r)-1/r Wherer = ρ/(ρ-1, Pi are parametric prices, and y is the consumer’s budget a) Solve for the Marshallian demand functions xi (P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity). b) Derive the Hicksian demand functions xih (P,u)a. Utility function of Mr. Haroon is given by Find the optimal quantities of the two commodities (X and Y) by using Lagrangian method, if it is given that price of commodity X is Rs. 5 per unit, price of commodity Y is Rs. 10 per unit and income of Mr. Haroon is equal to Rs. 1000. b. Using indifference map elucidates at which point Mr. Haroon would be able to achieve maximum utility.
- A typical consumer has a well-behaved preference structure for his consumption bundle which includes only two goods, A and B. assume that commodity A is normal and commodity B is inferior. By keeping commodity A on the x-axis and commodity B on the y-axis you are required to show the price decomposition for commodity B when $PB increases exogenously relative to $PA. Please Answer the question by using well labelled diagramsA consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle(8, 1). She is also willing to trade in 1 unit of x for 2 units of y when she is consumingbundle (4, 4). She is indifferent between these two bundles. Assuming that the utilityfunction is Cobb-Douglas of the form U(x,y)=xα yβ, where α and β are positiveconstants, what is the utility function for this consumer?A consumer has the following indirect utility function:U∗(Px, Py, M) = M2/2PxPy1. What is the consumers Marshallian demand for good x?2. What is the expenditure function?3. What is the Hicksian demand for good x?
