uppose the expenditure function is E(px. Py, U) = Ü(p + p} . Find the Hiicksian demand for good Y. %3D O a. h, = %3D O b. h, = %3D P, O c. h, %3D d. hy %3D Oe. hy %3D
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- Q1. Derive the Marshallian demand and indirect utility function for ?(?,?)=(0.3?‾‾√+0.7?√)2u(x,y)=(0.3x+0.7y)2. Q2. Derive the Hicksian demand and the expenditure function for ?(?,?)=(0.3?‾‾√+0.7?√)2u(x,y)=(0.3x+0.7y)2.A4Gary's demand function for good X is xG = 0.5 M/p where p is the price of the good and M denotes Gary's income. What is the slope of the Gary's compensated demand curve, assuming p= 7 and M = 209 dollarsConsider the following linear demand function where QD = quantity demanded, P = selling price, and Y = disposable income: QD = -36 - 2.1P + .24Y. The coefficient of Y (i.e., .24) indicates that (all other things being held constant): * for a one percent increase in disposable income, quantity demanded would increase by 0.24 percent for a one unit increase in disposable income, quantity demanded would increase by 2.1 units for a one percent increase in disposable income, quantity demanded would decline by 2.1 percent for a one percent increase in disposable income, quantity demanded would decline by 0.24 percent
- Consider a consumer with utility function u(x1, x2) = α_1x_1^( 2) + α_2x_2^( 2) where α1 > 0 and α2 > 0. Assume that p1, p2 > 0.? (a) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (b) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utilityConsider the utility functionU(x, y) = min{x, 2y}Find(a) the Marshallian demand functions for x and y,(b) the indirect utility function,(c) Use the expression for the indirect utility function that your found in part (b) to findthe expenditure function and the Hicksian demand for good x. [Note: Do not answerthis question by solving the expenditure minimization problem!]The consumer has an incom Mand a utility function of the form u (x1; x2) = aInx1 + (1 - a)Inx2 If the prices of the two goods are given by p1 and p2, derive the Hicksian demand functions for a given utility level U: Derive the expenditure function. Using the concept of duality, derive the indirect utility function.
- Consider the general supply function: Qs=60+5p-12Pl+10F Where Qs = quantity supplied, p = price of the commodity, pl = price of a key input in the production process, and F = number of firms producing the commodity. 1. Interpret the slope parameters on p, pl, ane F. 2. Derive the equation for the supply function when pI = $90 and F = 20. 3. Sketch the graph of the supply function in part b. At what price does the supply curve intersect the price axis? Give an interpretation of the price intercept of this supply curve. 4. Using the supply function from part b, calculate the quantity supplied when the price of the commodity is $300 and $500.Suppose the generalized demand function for good X is Qd=60-2Px+0.01M+7Pr a.Suppose M=40,000 and Pr=20 what is the direct demand function b.Suppose the supply function is Qs=-600+10Px, what are the equilibrium price and quantity? c.What happens to equilibrium price and quantity if other things remain the same as in part (b) but income increases to 52,000? d.What happens to equilibrium price and quantity if other things remain the same as in part (b) but the price of the related good decrease to 14? e.What happens to equilibrium price and quantity if other thing remain the same, income and price of related goods are at their original levels and supply shifts to Qs=-360+10Px?3. (a) If the demand function is P = 60 – Qfind an expression for TR in terms of Q.Differentiate TR with respect to Q to find a general expression for MR in terms of Q. Hence write down the exact value of MR at Q = 50.Calculate the value of TR when (a) Q = 50 (b) Q = 51 and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1)(b) The consumption function is C = 0.01Y2 + 0.8Y + 100 (i) Calculate the values of MPC and MPS when Y = 8.(ii) Use the fact that C + S = Y to obtain a formula for S in terms of Y. By differentiating this expression find the value of MPS at Y = 8 and verify that this agrees with your answer to part (a).
- Lan's utility function is U = xa y1-a where x denotes her consumption of good X, y denotes her consumption of good Y and a = 0.8. The price of good X is Px = 7, the price of good Y is Py = 14 and Lan's income is M = 338. If each price increases by 2 dollars, how much money must Lan be given to compensate her for the price increase?Denote the consumption of food by x and the consumption of all other goods by y. The demand for food as a function of prices and income is given by: Qx(px,py,W)=5W/8px. Suppose that W=100, px=3, and py=5. The change in consumption of food that is caused by a 2% increase in W is approximately: An increase of 2% in demand of y. There is no change. A decrease of 2% in demand of y. A decrease of 2% in demand of x. An increase of 2% in demand of x.A.) Without solving the expenditure minimization problem, recover the Hicksian demands and the expenditure function from the Mashallian demands and the indirect utility function.(B) Using the Slutsky equation find the total, income and substitution effect on smoothiebowls for a small increase in px when px = 2, py = 1, and I = 72
