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Angela's utility function is U(x1; x2) = (x1 + x2)3. Her indierence
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- Charlie's utility function is (1-a) U(xa, XB) = Ax“xr-) where A > 0 and a > 0Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.Consider the following utility functions. G(x,y) = x² + 3y² H(x,y) = (x+1)¹/2 + y + 1 L(x,y) = xey U(x,y) = In(x) + y² W(x,y) = 100 x - 4x² + 3 y Z(x,y) = (x)¹/² + y Which function or functions have strictly convex indifference curves (at every point where x>0 and y>0)?
- Consider the following utility functions: (1) u(x₁, x₂) = x₁ + 2x2. (2) u(x1, 1₂) = 2125 12.75 (3) u(x₁,1₂)=-1²-1₂. (4) u(x1, 1₂) min{x1, 2x2). For utility functions (1) to (3), give the equations of the indifference curves correspond- ing to utility level k, where 22 is expressed as a function of 2₁ and k. For utility functions (1) to (4), draw two indifference curves for each function. That is, draw four graphs (one for each utility function) and two indifference curves on each graph.Ann's utility function is U = q1q2/(q1 + q2). Solve for her optimal values of q1 and q2 as a function of p1, p2 and Y.Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.
- x9.359.65 He has an income of $72.00, and he faces these prices: (p1, p2) = (2.00, 7.00). Greg has the following utility function: u = Suppose that the price of x1 increases by $1.00. Calculate the compensating variation for this price change. Give your answer to two decimals. $Joyce consumes x1 and x2 together in fixed proportions. She always consumes 1 unit of x2 for 2 units of x1. What is the utility function that describes her preference?What kind of preferences are represented by a utility function of theform u(x1, x2) = √x1 + x2? What about the utility function v(x1, x2) =13x1 + 13x2?
- Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) isrepresented by the utility functionz; u(x, y) = xy + x + y Suppose now that Reese’s income is high relative to the prices of peanut butter andchocolate (more concretely, imagine I > px and I > py). What is Reese’s Marshalliandemand for peanut butter, x^∗(Px, Py, I)?Consider the following utility functions. G(x,y) = -1/[ min (6x,2y)+1] H(x,y) = min (6x,6y)² L(x,y) = min (6x,2y) - 10000000000 3 U(x,y) = min (3x, y)³ W(x,y) = min (6x, y)³ + 2 Z(x,y) = min (x,2y) Which of the above functions, if any, is homogeneous of degree 3? Select one or more: a. None. b. Z c. L d. G e. U f. W g. HQUESTION 1 For the utility function U = Qx0.73Qy(1-0.73) find the trade-off rate between good X and good Y at Qx= 3 and Qy=12 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).
