Consider an Edgeworth box economy in which the consumers have the Cobb- Douglas utility functions u₁(X11, X21) = x₁₁x11* and u₂(X12, X22) = x 12x12". Consumer i's endowments are (0) 1 (2;) > 0, for i = 1, 2. Solve for the equilibrium price ratio and allocation. How do these change with a differential change in 11?
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- If Philip's utility function is U=4 (41) 05+42. 0.5 what are his demand functions for the two goods? Let the price of q, be p,, let the price of q, be p2, and let income be Y. Philip's demand for q, as a function of p, and p, is 91 and his demand for good q, is (Properly format your expressions using the tools in the palette. Hover over tools to see keyboard shortcuts. Eg, a subscript oBunde's preferences are given by the utility function u(x1, x2) = x, + x2. For each of the following cases, decompose the price effects into the substitution and income effects using the Hicks-Allen decompositions. (For each part, use the given template to draw the constraints, and then use your completed graph to fill in the description. Enter any points in order from left to right as they would appear on the graph.) 20 15 10 5 10 15 20 (a) Suppose m = 120, P1 = 10, and p2 = 15. The price p1 then falls to 6, keeping p2 and m fixed. Given m = 120 and p, = 15, the budget B° is drawn for p, = 10. The utility-maximizing point on this budget is at A = given the linear preferences yielding utility y° = When p, falls to 6, the new budget is B" and the utility-maximizing point is C = ), yielding utility un = . The movement from A to C is the price effect of units of good 1. Removing income incrementally until Bunde can barely afford the old utility of at the new prices yields the line which…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+py
- Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand Functions0.1 0.9 Jordan has the utility function u(x₁, X2)=x₁₁¹×2. As this is a Cobb-Douglas function, we know that 10% of Jordan's income will be spent on good 1, and 90% of his income will be spent on good 2. We also know that the demand functions associated with this utility function are: x₁=0.1 m P1 m and x2=0.1. P2 Assume that Jordan is initially endowed with 200 units of good 1. If p₁ 5then what is the value of Jordan's endowment? What is Jordan's gross demand of good 1 when P₁ =5? What is Jordan's net demand when p₁ =5? Is Jordan a net buyer or seller? What happens to your answers to (a), (b), and (c) when the price of good 1 increases to 8? Explain your answer (hint: consider what happens to the demand for good 2).Suppose an individual has preferences over goods x and y, and their expenditure minimization problem has the following expenditure function: E(px, Py, U) = (px + 3p,)U. What is the person's Hicksian demand? O(h, hy) = (2p U, pU) O(h, hy) = (U, 3U) O(h, hy) = (Up,',Up,) O(hx, hy) = (3U, U) What is the individual's indirect utility? OV = 3p! p OV = P.+3p, OV = P Py OV = P.P
- Utility function U(X,Y)=(x^(3/4))(Y^(1/4)) 1)Suppose Px=2, Py=1, and Income is 100. What are the new levels of demand for X and Y? 2) Digrammatically show the income and substitution effect from 3 to 2 on the consumption of x. You must explicitly specify the optimal consumption bundles for the different sets of prices (appropriatly graph and label actual quantities) but you may qualitatively specify anything else deemed relevant. 3)Which effect (substitution or income) will move you along a given indifference curve? And for this question, do you move to the left or right along the given indifference curve and does this increase of decrese MRS. Also, explicitly specify what the MRS is equal to before and after you move along the indiferrence curve.Illustrate general equilibrium and the Laffer curve in the context of a repre- sentative consumer with a utility function: U(C,1) = In(C) + In(1) that he or she maximises subject to a constraint: C = w(1 – t)(h – 1) + T where w, h, l, C,t and T are wages, hours of time available, leisure, consumption, tax rate, and dividend income. The production function for this economy is given by Y = C + G = A(h – 1)'/2 %3D Assume that h = 1, A = 1 and that the government has a balanced budget. (b) Plot the government tax revenue for 0Pankti consumes two goods, x and y. Her utility function is given byU(x, y) = ln(xy).(a) Are Pankti’s preferences homothetic? Explain.(b) Suppose when Pankti’s income is 12, her optimal bundle consists of 2 units of x and 6units of good y. Without solving for Pankti’s Marshallian demands for x and y,determine how her consumption of x and y would change if her income doubled(holding constant the prices of the goods). Justify your answer as well as you are able.(c) Find an expression for Pankti’s indirect utility function, V (px, py, m), using themethod of Lagrange multipliers. Confirm your answer to part (b) using theMarshallian demands you derive in the process of solving the optimization process.(d) Suppose the price of good x is 2 and the price of good y is 2. Find Pankti’s utilitywhen her income is 24. Now suppose the price of good x doubles to 4. How much extraincome does Pankti need to obtain the same level of utility she had prior to the priceincrease?Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P, =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y O étv MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 F8 # $ % & 1 2 7 Q W E T Y tab S D F G caps lock C V M ft control option command つ つ エ B NSuppose that i's preferences over goods x and y are represented by the following utility function U₁(x, y)=x45¹5. Let m denote the consumer's income, p denote the price of good x and let the price of good y equal 1. A) Find the Marshallian demand functions for goods x and y. B) Show how each of the demand function is affected by a change in the price of good x. C) Which of the goods is an inferior good?Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3SEE MORE QUESTIONS