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- Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…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. HSuppose a consumer's utility is given by: u (x1, x2) = a/xT + b/x2 Where a= 8, and b = 4 %3D What is the value of MU1 (x1, X2)when x1=9 and x2=8. (Note: The answer may not be a whole number, so round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)
- Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.Consider the following utility functions. G(x,y) = -1/[ min (6x, 2y)+1] H(x,y) = min (6x,6y) L(x,y) = min (6x,2y) - 10000000000 U(x,y) = min (3x, y) W(x,y) = min (6x, y) Z(x,y) = min (x,2y) Select the function or functions, if any, representing the same preferences as function U?1. For each of the following three utility functions below, find the demand function by explicitly solving each utility maximization problem. (a) u(x1,x2) = xx. (b) u(x1, x2) = Inx1+2lnx2. (c) u(x1,x2) = x7x3.
- The consumer’s utility function is u(x1, x2) = 2√x1 + √(x2/4) (a) Determine the equilibrium condition for MRS21 and prices p1, p2. (b) Express the general form of D1(p1, p2, m), D2(p1, p2, m). (c) Calculate the desired amounts x1, x2 for p1 = 8, p2 = 2, m = 80. (d) Express the general form of income elasticity for commodity x1. Please show working step by step for b,c,d with final values of solution like in aUpon graduating from UT this May, you take on a management position working at UtMax theater. You will consider the utility of seeing performance over 1 month, and suppose that at a regular price of $$$ per ticket (my assigned ticket price is 145), customers will see no performance, however with the price reduced by $5, customers will see one performance per month and when reduced by $10, customers will see two performances. As long as the number performances, x, is small, your demand function for performance can be modeled by p=D(x). Write down your demand function.Problem 3 (10 points; 5 points for each part): Richard has a total utility function of: TU = 10q₁q₁²+24q2q2² +9192, where q₁ and q2 are goods. Richard is currently consuming at q₁ = 4 and q₂ = 6, which is also his utility maximizing consumption level. (Richard's optimal point is an interior solution). (a) How much additional utility would Richard receive if he were to increase his consumption of q2 from 6 to 7? (5 points). (b) How much q2 is Richard willing to pay (in terms of q2) in order to consume the 5th unit of q₁? (5 points).
- A consumer's preferences are represented by the following utility function: u(x, y) = 2 T+ Vỹ +7 1. Recall that for any two bundles A = (TA, YA) and B (TB, YB) the following equivalence then holds AEB u(A)> u (B) Which of the two bundles (x1,Yı) = (9,4) or (x2, Y2) = (4,9) does the consumer prefer? 2. Take as given for now that this utility function represents a consumer with strictly convex preferences. Also remember that preferences are strictly convex when for any three bundles A, B, and C, if B E A and C E A then aB +(1 – a)C > A for any a E (0, 1). Use this information and your answer to (1) to determine which of the two bundles (03, Y3) = (7,6) or (x2, Y2) = (4, 9) the consumer prefers. Verify your answer. 3. Derive an expression for the marginal rate of substitution. Interpret the MRS. What is the MRS at the point (x3, Y3) = (7,6)? 4. Derive an equation for the indifference curve through the bundle (x2,Y2) = (4,9). With an equation it is meant: y as a function of x, y(x), such…For the utility function U = Qx0.31Qy(1-0.31) find the trade-off rate between good X and good Y at Qx= 7 and Qy=17 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).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?