Suppose the preferences of the consumer in (1) were instead described by U(x₁, x₂) = 2x₁ + x₂. Compute the Slutsky substitution and income effects of this price change.
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- Suppose the preferences of an individual are represented by a quasilinear utility function: U(x, y) = In(x) + 3y a) Initially, Px=1, Py=6 and 1=102. Then, the price of x increases to 2 (Px=2). Calculate the changes in the demand for x. Please also calculate the substitution and income effects of the change in Px on x. (Hint: since the change in price is not small, you cannot use the Slutsky equation. You need to have numbers instead of functions as the answer.) B)Please also calculate the substitution and income effects of the change in Pr on y. C) Instead of doubling to 2, suppose Px is only increased by a small amount. Use the Slutsky equation to find the substitution and income effects of the change in the price of x on x. Compare your result to (a). Explain why there's no income effect of the change in Pa On X. Show your result on an indifference curve. d) Use the Slutsky equation to find the substitution and income effect of the change in Px on y. Compare your result to (b).Suppose the weighted marginal utility for two goods x and y at a position of consumer equilibrium 70. If the price of good x is r10 and the relevant marginal utility for y is 140 what is the price of good y and the relevant marginal utility for xIf the demand function face by the consumer for good X is given by X=15+MP-120 Where X = Quantity demanded, M = income and P = Price of product X. Assume his original income is Kshs. 3200 per month and price of good X has increased from Kshs. 10 per unit to Kshs. 20 per unit. Calculate the magnitude of total effect (TE), substitution effect (SE) and income effect (IE) resulting from this change in price.
- Laura's preferences over commodities X₁ and x₂ can be represented by U(x₁,x2)=min{3x₁, x₂}. She maximizes her utility subject to her budget constraint. Suppose there is an increase in p1. There are both income and substitution effects of this price change. There is an income effect but not a substitution effect of this price change. There is a substitution effect but not an income effect of this price change. It is unclear whether the consumer will buy more or less x1 as a result of the increase in p1.Solve the attachmentCompute marginal utilities and marginal rate of substitution for each of the utility functions given below. a) U(X,Y)= 1- e-ax -e-by b) U(X,Y)= XY + 3X + 5Y c) U(X,Y)= (0.3Xm +0.78m)/1 X1-a y1-b d) U(X,Y)= + 1-a 1-b
- Mr. Abdulah enjoys Coffee (K) and Tea (T), with the utility function U (K, T) = 3K + 4T. Question: - If the income drops to IDR 10, what effect will it have? - When does the Demand curve occur? Show in the picture.3. A consumer is faced with a utility function u(x, y) = 4x² + 3xy + y² And his budget constraint is given by ln( xy) = 5. a) Find the optimal values of x and y b) Find the value of the shadow price c) Interpret the value of lambda. Does it make economic sense? d) Other than completeness, monotonicity and transitivity, discuss the other three axioms of consumer preferences. e) Using practical examples discuss the duality principle as it relates to both the firm and households.Alice receives an allowance of 500 dollars that she spends on buying snacks (S) and tea (T). The price of each snack is 10 dollars and the price of each tea is 5 dollars. Her utility is given by: U (S, T) = 2S³/4 +T3/4 (a) Find her marginal rate of substitution (MRS) between S and T. (b) Write Alice's budget constraint. (c) Find Alice's optimal consumption and the optimal A. (d) What is her new consumption if the price of tea becomes 10 dollars? Note: numeric solutions for questions (c) and (d) are not integers.
- Determine the monotonicity and convexity of these preferences and briefly define what they mean. Calculate and interpret the marginal rate of substitution (MRS(x1,x2)) between the two goods for this consumer at the bundle(x1, x2)=(2,1).Consider the following 6 utility functions: U1 = Vx + 2y U2 = v2x + Vy Uz = 2x2 + y? + Vy U4 2 Ug = min(x,y)+; 2 Us = 2 In(x) + In(y) %3D a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and determine whether monotonicity and convexity are met.A consumer with the utility function U(x₁, x₂) = x³x₂ faces prices p₁ = $4, P₂ = $5 and has an income of $100. Suppose the price of the first good rises to $8. Compute the Slutsky substitution and income effects of this price change.
