This questions examines the Lump Sum Principle on subsidies. Consider an indi- vidual with a Cobb-Douglas utility function U(x, y) = x¹/²y¹/2, and faces prices pr, Py with an income of $1. (a) First, find the optimal demand for x and y and compute the indirect utility function, V (Pa, Py, I). (b) Now let. No = 1 and n.. - 4. Use the expenditure function E(p. Dor. U). to calculate
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- Which of the following elasticities can be generated by a Marshallian demand function ga (Pa, Py, I) if the good r is inferior but not a giffen good and good z and good y are gross substitutes? (a) er.p = -0.15, (b) er.pr -0.25, = (c) €x.pz (d) er.p = 0.15, (e) ezpz = -0.25, = = 0.5, (a) -1 (b) -1/2 (c) 0 (d) 1/2 (e) 1 еx,py ex.py ex.py = -0.33, Crpy = 0.15, ex.py = 0.15, erl= -0.15 -0.25, ex, I = -0.25 ex,1 = -0.17 Cr,l = 0.15 = 3 = 0.75, ex,1 = -0.5 If an individual has the following utility function, U(x, y) = ln(x)+ln(y), then 2e1px + er.pyer is equal to:Suppose the demand for a good was given by the function: QD = 350 - 0.4PCalculate the choke price of this demand function.(Do not include a $ sign in your response.)Q = a + bP + cM In the demand function above, Q is quantity demanded, P is the price of this good, and M is consumer income. The parameter, b, is the effect on Q of change in P: b ΔQ /ΔΡ Using this relationship for b, find an expression for the price elasticity of demand (E). Select one: O a. E = b(Q/P) O b. E = b(P/Q) %3D O c. E = b(AQ /AP) %3D O d. E = b + (P/Q)
- I 3] Consider the utility function U = 2√√9₁ + 3√√92. a) Solve for the uncompensated (Marshallian) demand for good #1 as possible functions of P₁, P2, and Y. b) Solve for the uncompensated price elasticity of demand for good #1. c) Solve for the uncompensated income elasticity of demand for good #1. d) Solve for the compensated (Hicksian) demand for good #1 as possible functions of P₁, P2, and U.Given the demand function Q=500-3P-2PA+0.01Ywhere P=20, PA=30 and Y=5000, finda)price elasticity of demand b)the cross price elasticity of demandc) if the income rises by 5%, calculate the correspinding percentage change in demand. Is the good inferior or superior?. True or false? If the demand function is x1 = −p1, then the inversedemand function is x = −1/p1.
- A particular commodity has a price-demand equation given by p = √18,444 - 417x, where x is the amount in pounds of the commodity demanded when the price is p dollars per pound. (a) Find consumers' surplus if the equilibrium quantity is 40 pounds. (Round your answer to the nearest cent if necessary.) (b) Find consumers' surplus if the equilibrium price is 17 dollars. (Round your answer to the nearest cent if necessary.) $If the individual demand function for good X is given by X = 100-2px-4py +1, where px = PY = $20 and I = $40, what is the cross-price elasticity of demand? $10,Consider the following demand function for good 'X': Q = 9-0.1p, - Py + 0.01p, + 0.001Y, where Price of a related good, P= $3 Price of a related good, P, = $275 Own price, P,= $30 Quantity demanded = 35.75 Consumer income, Y = $30,000 The income elasticity of demand, E, when eguilibrium quantity is 35.75 units and income is $30,000 is equal to. (Enter a numeric response using a real number rounded to three decimal places.) O etv MacBook Air DII DD 80 F10 F7 F8 F4 F5 F2 F3 EI $ % & ! @ 7 9 1 3 4 Q W E R T Y D F H J K A C V N M command tion command .. .- V - * 00 * :
- The price-demand equation for a particular flashlight is given by p = 118 - 0.002x, where x is the number of flashlights demanded when the price is p dollars each. The flashlight manufacturers will produce no flashlights if the price is $79 or less, and they will market 5,500 flashlights when the price is $101 per flashlight. (Assume the price-supply equation is linear.) (a) Find the consumers' surplus for this commodity. $ (b) Find the producers' surplus for this commodity. $-x2 + 324. Find the consumers' The demand function for a particular product is given by the function D(x) surplus if xE = 9 units.I Nam's Marshallian demand function for good X and Y is given by: X* = Suppose that Px-3, a = 0.7, B = 0.3 and I-18 2Px(0+B) The own-price elasticity of demand of good X is_