Suppose E(pa, Py, U) = 2√ PapyU with U > 0. Then, (a) y is a net complement for x and x is a net substitute for y (b) y is a net substitute for x and x is a net substitute for y (c) y is a net complement for x and x is a net complement for y (d) y is a net substitute for x and x is a net complement for y
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- If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y)=LY+2L a. b. C. Calculate the demand function for L and show it on a graph (L vs W). Calculate the labor supply (H) and show it on a graph (H vs W). What will happen to L, Y and H if the wage per hour (W) will decrease? =Please solve all parts (d and e) Find the marginal rate of substitution of y for x [MRS(x,y)] for the following utility functions
- Disscuss the Marginal rate of substitutionCompute marginal utilities and marginal rate of substitution for each of the utility functions given below. In cach case. explain whether the assumptions of diminishing marginal utility and diminishing marginal rate of substitution are satisfied or not. a) U(X,Y)= 2x-yi b) U(X,Y) = XY +3X + 5Y c) U(X,Y) = (0.3X + 0.7Y") d) U(X,Y) = In (5VX + 2VT) %3D %3D %3DSuppose 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?
- Suppose that the utility derived by the consumer from x units of the first commodity and y units of the second commodity is given by the utility function U(x, y) = 10x0.6y0.4 The first commodity costs $ 20 per unit and the second $ 30 per unit. Both x and y are continuous variables. a) Find the function equation for the cost function C(x, y). Draw a contour plot of C (x, y) showing the contour lines of levels 500, 600 and 700. b) Add a contour plot of U(x, y) to this graph in which you draw contour lines of levels 100, 150 and 200. You are allowed to use the graphical calculator to graph a function from its explicit function equation. c) The consumer wants to maximize utility with a budget of $ 600. Indicate the correct option below: The maximum utility is below 100. The maximum utility is between 100 and 150. The maximum utility is larger than 150. Explain your answer based on the graph you made so far; d) Estimate how many units of each commodity the consumer should buy to minimize…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.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. (b) Calculate consumers’ income elasticity as a function of the parameters. (c) Anaya is targeting a market whose income is expected to double over the next five years.Explain whether she should expect the demand for chargers to increase or decrease, andby how much, using the language of normal, inferior, luxury, and necessity goods. (d) Calculate the cross-price elasticity ofCwith respect toPF. (e)…
- If Jackson's preferences over consumption bundles can be represented by the utility function U(X, Y) = 2X + Y, what will Jackson's optimal bundle, (X*,Y*), be when the price of X is px = 3, the price of Y is py = 1, and Jackson's income is I = 150? (a) (110,0) (b) (0, 150) (c) (0,80) (d) (50, 0) (e) (30,60)Sharon spends her time (16h) between leisure (L) and work and he consume Y product from his working income (P=1). Assume that she gets W$ per hour of working (W>0) and has the following utility function: U (L, Y) =LY 4Y. a.Calculate the demand function for L. and show it on a graph (L. vs W). b. Calculate the labor supply (H) and show it on a graph (H vs W). c.What will happen to L. Y and H if the wage per hour (W) will decrease?3 The following utility function is known as CES (constant elasticity of substitution) function: U (x, y) = (ax° + By')'/º, where a > 0, B > 0 %3D a) Is this function homothetic? b) How does the MRSY depend on the ratio x/y? Specifically, show that the MRSxy is strictly decreasing in the ratio x/y for all values d 1 and constant for 8 = 1. (Hint: take the derivative of the MRS with respect to the ratio x/y as z = and take the derivative with respect to z) x,y x/y c) Show that if x = y, the MRS of this function depends only on the ratio /B.