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- Suppose Marcel's preferences over consumption bundles (X, Y) can be represented by the utility function U(X, Y) = X³Y. Which of the following expressions gives Marcel's Marshallian demand? (a) (X*,Y*) = ( 31 3px+py' (b) (X*,Y*) = (px (PX+py)) (d) (X*,Y*) : = 3px' +py) 3px+py (c) (X*,Y*) = (-1,0) Ipx px (px+py)' py (py+PX) 1 I 3 I 4px' 4 py (e) (X*,Y*) = = ( px + 4py ² : 31 px +4py' 4px+pySuppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the quantity of pizza demanded, P is the price of a pizza, and Pb is the price of a burrito. What is the slope of this demand function, and what information does the slope provide?..(2) Lisa can buy either whole chickens or chicken wings at her local supermarket. Her utility function over whole chickens and chicken wings is U(xc,Xw) = 2xc + Xw, where x, and xw are chickens and chicken wings, respectively. What is her demand function xc (pc, Pw, m) for chickens?
- Consider the following utility function U(x1, x2) = Min{x1, X2} + 1/2Max{x1, x2} Calculate the Marshallian demand for both goodsSuppose you have the following indirect utility function: V(Pa, Py, I) = In PxPy What are marshallian demands for x and y? I (a) (9x9y) = (22) (b) (9,9y) = (In, In 2) (c) (9, 9y) = (exp(2p/py), exp(2ppy)) I (d) (9x, gy) = (2pr+py' px+2py) What is the expenditure function for the associated expenditure minimization problem? (a) E(pa, Py, U) = (P + Py) ln(U) (b) E(pa, Py, U) = √exp(U)Papy (c) E(pa, Py, U)= (p²+p²) In(U) (d) E(pa, Py, U) = exp(U)²papy What are the individual's Hicksian demands for goods x and y? (a) (h₂, hy) = ((BU)¹/², (PU) ¹/²) (b) (ha, hy) = (RU, DU) (c) (ha, hy) = ((2 exp(U))¹/², (exp(U))¹/²) -1/2 (d) (hx, hy) = ((P₂PzU)−¹/², (P₂PzU)-¹/2) Are x and y complements or substitutes?a)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese meals and use the utility maximization conditions to find the demand for Vietnamese food of the typical consumer (keep in mind that since utility is quasi-linear, you can find demand without information about the consumer’s weekly budget). b) Sum across consumers to find the weekly market demand for Vietnamese meals in NYC.
- 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"?For a demand function Qd = f (P), a change in price causes a change in the quantity demanded. There are other five (5) variables, enumerate and explain each variable influencing demand in the general demand function. These are fixed at specific values for a given demand equation.From the demand function Qdx = 22 + 2Px (Px is given in dollars), derive (a) the individual’s demand schedule fast.
- Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers (C). Her market research has found that consumer demand for this product can beexpressed as a function of the price of the charger itself (PC), the price of phones (PF), andthe consmer’s income (I). Consumer demand can be described by the function C(PC, PF, I) =(i−10PC)/ (PF) Suppose her chargers come in all different capacities to meet any quantity demanded, so youdon’t need to worry about restricting C to whole numbers for this problem. (a) Does this product satisfy the law of demand?Explain.Given the utility function Log Y = 0.42logX1 + 0.58logX2 Find the demand functionConsider the utility function: U(x,y)= -4(3x-12)² - (2y-10)² Determine the marginal utility for the two commodities