Marvin has a Cobb - Douglas utility function(U= 90.5 1 q0.5 2), his income is Y = 10, and he faces prices of p2 = 2. (a) Find the uncompensated demand (marshallian demand) curves for good 1. (b) Find the compensated demand (hicksian demand) curves for good 1. (c) Find the expenditure function (E(p1, p2, u)) From now on, suppose the price of good 1 increases from p1 = 1, to p '1 = 2 (d) Find the change in consumer surplus(ACS), Using uncompensated demand (marshallian demand) function. (e) Find the compensating variation (CV). (f) Find the compensating variation (EV).
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- 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)Charlie's utility function is (1-a) AXA B Ax^x U(x4, XB) = %3D where A > 0 and a > 0 are positive parameters. What is the own price elasticity of Demand for good XA O infinite O-2 O-1I 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.
- . Economists often say that goods tend to have more elastic demand when they have lots of close χδ = α + (1 - a) substitutes. Use the CES utility function U(x, y) to show that the own-price elasticity of demand for good X gets larger (in absolute value) as the elasticity of substitution gets larger.42) If an increase in income results in a rightward parallel shift of the demand curve, then at any given price, the price elasticity of demand will have Alincreased in absolute terms. B) decreased in absolute terms. C) remained unchanged. D) increased, decreased or stayed the same. It cannot be determined. 43) If the demand function for orange juice is expressed as Q = 2000 ( 500p, where Q is quantity in gallons and p is price per gallon measured in dollars, then the demand for orange juice has a unitary elasticity when price equals A) SO. B) S1. (C) $2. D) $4. 2.00 0-S00 (3) 2000-1000 44) If the demand curve for orange juice is expressed as Q=2000 - 500p, where Q is measured in gallons and p is measured in dollars, then at the price of $3, elasticity equals A)-0.33. (BY-3. C) -9. D) -17.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.)
- -x2 + 324. Find the consumers' The demand function for a particular product is given by the function D(x) surplus if xE = 9 units.Suppose Ashley has the utility over two goods X and Y as U(X,Y)= XY and the prices and income are p = 3, Py = 5 and I = 50. Let s, and sy be the shares of income spent on good X and good Y, respectively, and let er, and ey, be the income elasticities of demand for goods X and Y, respectively. Then, Szer,+Syey, is equal to (a) 2 (b) 1 CORRECT ANSWER (c) 0 (d) -1 (e) Not enough informationEx. 1 two goods. Market prices are given by p (PL.P2) and the consumer's income is given by y. A consumer has utility function U(11, 12) = 1*2 + 8 where zį and r2 are the Set up the utility maximization problem and derive the Walrasian demand for the two goods. • Compute the elasticity of the demand for good r2 with respect to income y. Which kind of good is good z2? Compute the indirect utility function v(P: ) and verify its main properties. Ex. 2 A firm produces output Z combining input X and Y according to the following technology: Z = f (X,Y) = K (aX² + (1-a) Y) The cost of input X is wx, while the cost of input Y is wy. The price of output Z is p. The firm is price-taker both on the input markets and on the output market. Compute the conditional input demand function. Compute the elasticity of substitution. Interpret this quantity. • Compute the cost function. How does the cost function marginally change if you modify the price of one input? Explain.
- Demand for Magnum Ice Cream is given by an equation as Q = 70 – 10P + 4 Px + 50 I Where, Q = Quantity of Magnum demanded, P = Price of Magnum Ice Cream, Px = Price of Walls Ice Cream, I = Per Capita Incomea. Assume P = Rs 100, Px = Rs 120 and I = Rs 25 (Rs in thousands). Calculate (i) Price Elasticity of Demand(ii) Cross Price Elasticity of Demand(iii) Income Elasticity of DemandQues- D= f (PX) is a general form of demand function, does not explain the nature and magnitude of the relationship between dependent and independent variable? How will you explain bivariate and multivariate demand functions with reference to price, income, price of related goods (substitute goods in specific linear and in-linear form of demand function?Consider the demand function for good1, Q1 = 681 - P1 + 0.75* P2 - 0.5* P3 + 0.05*Y Where, price of good1 (P1) is 200, price of good2 (P2) is 92, price of good3 (P3) is 399, and income (Y) is 18937; (i) Find the price elasticity of demand (PED). (Give your answer to two decimal places) (ii) Find the income elasticity of demand (YED) (Give your answer to two decimal places). (iii) Find the cross price elasticity of demand (XED) between good1 and good2. (Give your answer to east two decimal places) (iv) Find the cross price elasticity of demand (XED) between good 1 and good 3. (Give your answer to two decimal places) (v) Estimate the percentage change in the demand for good1 resulting from a 10% decrease in the price of good3. (Give your answer to two decimal places, if required and do not use % sign in your answer)