Consider a consumer with expenditure function e(p, u) = p2u - √ Suppose that the consumer has wealth 4. Initially, prices are (3,2). (a) What value of a would make the consumer indifferent between a fall in prices to (1,1) with wealth remaining at 4 and an increase in wealth of 2 with prices remaining at (3, 2)? How is this conceptually related to the compensating or equivalent variation? (You do not have to do any additional calculations to answer the second part of the question.) (b) Find the substitution and income effects on Good 1 associated with a marginal increase in the price of Good 2 when prices are (3,2).
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- Answer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSEQUESTION 1 Qx0.65Qy(1-0.65) and the budget 127 = 6Qx + 6Qy find the CHANGE in optimal consumption of Y if the price of X increases by a factor of For the utility function U = 1.8. 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).1. Consider the utility function given by u (x1, x2) = x1x3, and budget constraint given by P1x1 + P2x2 = w. (a) Solve the EMP to find the Hicksian demand function, h (p, u). (b) Find the expenditure function e (p, u). (c) Recover h (p, u) from e (p, u). (d) Noting that the indirect utility function corresponding to the UMP for this form is 4w3 v (P1, P2, w): 27p1p3' demonstrate that v (.) and e (.) are inverses of each other. (e) Using only the indirect utility function above, recover the optimal consumption bundle of the UMP (i.e., Walrasian demand function). (f) Using your answer to (e), identify the substitution effect on the quantity demanded of good 1 of a change in the price of good 1. 1; and consider the Hicksian demand curve for good 1 corresponding to , and Walrasian demand curve for good 1 corresponding to w = 1. At what price and quantity for good 1 do they intersect? Which is steeper at this point of intersection? (g) Assume P2 What does that signify? (h) Using your…
- For the utility function U=Qx0.370,(1-0.37) and the budget 194 140x+6Qy find the CHANGE in optimal consumption of X if income increases by a factor of 1.4. 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).Consider a consumer with indirect utility function v(p, w) = w - B1p1 - B2p2 √P1P2 where 3₁ and 32 are nonnegative constants. (a) Find the consumer's expenditure function. (b) Find the Hicksian and Marshallian demands for Good 1. (c) Find expressions for the substitution and income effects on Good 1 associated with a marginal increase in the price of Good 2. (d) Suppose that the price of good 1 changes from pi to kp₁ where 0 < k < 1. Find the compensating variation of this price change.Question 1 Consider a consumer with a utility function of U(X,,X2, ... , Xn) = II-1 X , a; > 0, i = 1,2,3, ...,n. P; is a price of 1 unit of the i-th good. Assuming that the consumer has the total budget of $M, derive his optimal consumption bundles in the following procedure. (a) Set up the consumer's utility maximization program with a Lagrangean multiplier. (b) What is an economic intuition of the Lagrangean multiplier? (c) Assuming an interior solution, get all the FOCS. (d) Find an optimal consumption bundle while specifying each step required to get the solution. (e) Characterize the maximized utility as a function of $M and the parameters. What does it look like? (f) Find an exact value of the Lagrangean multiplier.
- QUESTION 1 0.68Qy(1-0.68) and the budget 181 = 6Qx + 8Qy find the optimal consumption of X. 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). For the utility function U = QxIf Jackson's preferences over consumption bundles can be represented by the utility function U(X, Y) = 2X + Y, what will Jackson's optimal bundle, (X*,Y*), be when the price of X is px = 3, the price of Y is py = 1, and Jackson's income is I = 150? (a) (110,0) (b) (0, 150) (c) (0,80) (d) (50, 0) (e) (30,60)QUESTION 1 x0.80Qy(1-0.80); and the budget 153 = 11Qx + 12Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.9. as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1). Qx For the utility function U = Please enter your response
- 3. Consider the following utility function, u (21, x2) = min V#1, Varz), where a > 0 Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? Show two different ways to derive the Hicksian demand functions. (b) Does the Hicksian demand increase with price?Given a consumer has a money budget M = 90 and utility function ? ( ? , ?) = ? 1/4? 1 / 2 If she consumes two goods x and y with prices given by ? = 2 and ? = 4 state the ? ? budget constraint equation. Determine the utility maximizing quantities X and Y for the consumerThe utility that Elena receives by consuming food F and clothing C is given by U(F,C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is£22. MUF = C+1 and MUc = F.(i) Define the term Marginal Rate of Substitution (MRS). (ii) Find the utility maximizing values of C and F for the numerical values given above(Hint: You can assume interior solution). (ili) Now suppose that price of C and Elena's income remain unchanged at £2 per unitand £22, respectively, while the price of F varies. Find the equation of the demand forF as a function of the unit price of F (PF).