3. (10 pts) John consumes two goods, X1 and 22. His preferences are represented by the...
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?
Molly consumes two goods, good x and good y and her preferences are represented by the utility function U (x, y) = 1/2x^2 + 4y. 1. Draw (sketch) Molly’s indifference curves for U(x,y) = 10, U(x,y) = 16, U(x,y) = 24 and for U(x,y) = 32.5. 2. Do Molly’s preferences satisfy strict monotonicity? Explain briefly 3. Do the indifference curves you’ve drawn reflect preferences that are convex? Explain briefly
QUESTION 11 Suppose there are two goods, X1 and x2, and your preferences are represented by the following utility function: , u(x1,x2) = x1/4xz.! The price, P1, for good x1, is 2.5 and the price, P2, for good x2, is 3.5. You have units of money (M) of 60. Compute the consumer's optimal consumption of x1and x2 Enter x1 only here:
4. Suppose Michelle's tastes for haircuts (x1) and spending on other goods (x2) per year can be represented by the separable utility function u(xı,x2) 600x1% +2x2. (3 marks) (a) Derive an expression for Michelle's marginal rate of substitution (MRS). (b) Derive expressions for Michelle's optimal bundle of xi and x2 by simply using the fact that, at any interior solution, MRS--pi/pz. (4 marks) (c) What slope does Michelle's demand curve for haircuts have (e.g. downward-sloping, upward-sloping, horizontal, vertical)? (2 marks)...
Suppose a consumer’s preferences over goods 1 and 2 are represented by the utility function U(x1, x2) = (x1 + x2) 3 . Draw an indifference curve for this consumer and indicate its slope.
Donald consumes goods x1 and x2. His utility function is U(x1, x2) = x1(x2)3. He is endowed with 43 units of x1 and 7 units of x2. The price of x1 is $1 and the price of x2 is $3. Find his net demand for x1. a) b) c) d) e)
John consumes two goods, X and Y and has an income of $25. Price of good X is S3 per unit and price of good Y is $2 per unit. John's utility function is given by U (X, Y) = 0.5 XY. The marginal utility of X, MUx 0.5Y and the marginal utility of Y, MUy 0.5X. (a) Determine the optimal values of X and Y that will maximize John's utility. (7 marks) (b) Calculate the total utility at the...
Suppose there are two consumption goods and preferences of a consumer can be represented by the following utility function: ; a) Derive the Marshallian demand function of this consumer. b) Calculate and intuitively interpret the elasticity of substitution. d/11027(0 - 1) + 10) = (2x Iz)n (0<a <1:0 +p<1)
John has the following utility function that represents his preferences over food (x) and housing (y) (his only two expenses) and marginal utilities: มุ4 for a level of wealth W and prices of food and housing P y respectively. Using the results from the previous homework answer the following questions Write down the Engel Curve for both goods and graph them 2) Assume W-10 and the price of food changes from 1 to 3 while the price of housing remains...
Expecially b,c. Thanks 3. Albert consumes two goods: Chips (C) and DVDs (D). Albert's preferences can be described by the utility function U(C,D) = 50 + 3D!. Albert has income M and the two goods have prices Pc and P» (chips and dvds). (a) Write out the expression for Albert's marginal rate of substitution (or slope of Albert's indifference curves when good C is graphed on the horizontal axis). (2 marks) (b) Write out Albert's utility maximization problem and derive...