2. Assume you spend your entire income on two goods X & Y with prices given as Px & Py, respectively. Prices and income (1) are exogenous and positive. Given that U= X'Y', derive the Hicksian demand function for good Y.
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- 1. 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 = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good. 2. 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= X2Y2 , derive the Hicksian demand function for good Y.3. Suppose that initially PX = 2, PY = 8, I = 96 and the Marshallian demand function for good Y is given by Y∗ = (0.5I/ PY)+(0.5PX/PY)− 0.5. Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (XA,YA) = X0.25Y0.75, UB (XB,YB) = X0.75Y 0.25Show that pareto-improvement is possible if,…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 = X + Y, derive the Marshallian demand function for good Y and evaluate the type of good. Assume you spend your entire income on two goods X & Ywith prices given as Px & Py, respectively. Prices and income (I) are exogenous and positive. Given that U= X²Y², derive the Hicksian demand function for good Y. Suppose that initially Px = 2, P = 8, I = 96 and the Marshallian demand function for good Y is given by . Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.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 = X² + Y?, derive the Marshallian demand function for good Y and evaluate the type of good.
- Julian is interested in only two goods: good X and good Y and has M dollars to spend (and always spends it all). His uncle Paul is rich and he offered him 1000 dollars as a present but Julian did not take it and chose to just spend his own money. Julian's demand function for good X and the demand function for good Y are given respectively by XJ = 32800/(10Px + Py) and Y₁ = 3280/(10Px + Py). What is Julian's spending money "M"?Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to find that of Y) when your preferences are represented by the utility function U = x + xy + y. Is X normal good? Can you confirm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derivedConsider two consumers, A and B, who consume two goods, x and y. Assume that the utility function for A is U₁ = A₁ and the utility function for B is UB = XBYB. Consumer A is endowed with 10 units of x an 10 units of y. Consumer B is endowed with 10 units of x and 40 units of y. Assume the price of y is set to $1. What is the expression for Consumer A's demand for x? XA 10p, +10 Pr 10p, +40 Pr 10pz +10 4pz 10p, +40 4pz
- Consider a market with two goods, x and z. The consumer’s utility function is U = x^0.2z^0.8 A. Derive the demand function for x and z. B. Let ? = 2, = 4 and = 50. Find the equilibrium quantities demanded of x and z.You are choosing between two goods, X and Y, and your marginal utility from each is as shown in the table below. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase to maximize utility? What total utility will you realize? Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? Using the two prices and quantities for X, derive a demand schedule (price–quantity-demanded table) for X.Let a1 and x2 denote the quantities consumed. The consumer's preferences are represented by the utility function: U (r1, 22) = V+ VT2. Suppose the consumer has income m =100 and that the prices for the two goods are pi -2 and p2=8. Calculate the optimal quantity demanded for good 1.
- The demand function for a particular good is x = a + bp. What are the associated direct and indirect utility functions?Economics Suppose that an individual receives utility from two goods X and Y and his utility function is given by: u = -1/X –1/Y. a) Derive the Marshallian and Hicksian demand functions for X and Y. b) How would you determine whether X and Y are gross substitutes or gross complements? c) How would you determine whether X and Y are net substitutes or net complements?For the below questions, consider a consumer that consumes two goods, x and z with the following utility function. ū=x0.75 0.25 Suppose initial values for income and the prices of goods x and z are y = 100, Px = 5, and Pz= 15 respectively, then the price of good x increases to Px = 10. What is the magnitude of the Total Effect? TE = -9 TE = 7.5 TE = -7.5 TE = 9