Consider the utility function of U(X,Y) = X0.2Y0.4 Derive the Marshallian demand curve for X Derive...

Consider the utility function of U(X,Y) = X^0.2Y^0.4

Derive the Marshallian demand curve for X
Derive the Hicksan demand curve for X
What is the own-price elasticity for X?
What is the income elasticity of X?
What is the price elasticity of X with respect to y (P_y)
If the income level is 120, then what is the P_xthat maximizes total spending
Show that Slutsky equation holds
Show that e_x,px+e_x,py+e_x,I=0. What does it mean?
Show that Engle Aggregation holds. What does it mean?
Show that Cournot Aggregation holds. What does it mean?

Expert Solution

Rahul Sunny answered 8 months ago

Suppose Mike’s utility function is u(x,y)=2lnx +lny. 1. Derive the demand functions. 2. Is y a...

Suppose Mike’s utility function is u(x,y)=2lnx +lny. 1. Derive the demand functions. 2. Is y a Normal good? 3. Is x an ordinary good? 4. Assume the price of x is initially 1 dollar, and the price of y is also 1 dollar. Given that income is 9, if the price of x doubles to 2 dollars, decompose the change in consumption of x into substitution effect and income effect. Illustrate your answer with a graph. 5. Now, given the...

1. Suppose Mike’s utility function is u(x,y)=2lnx +lny. a. Derive the demand functions. b. Is y...

1. Suppose Mike’s utility function is u(x,y)=2lnx +lny. a. Derive the demand functions. b. Is y a Normal good? c. Is x an ordinary good? d. Assume the price of x is initially 1 dollar, and the price of y is also 1 dollar. Given that income is 9, if the price of x doubles to 2 dollars, decompose the change in consumption of x into substitution effect and income effect. Illustrate your answer with a graph. e. Now, given...

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy...

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy + 2,000. Tammy’s utility function is U(x, y) = xy(1 - xy). Oral’s utility function is -1/(10 + xy. Billy’s utility function is U(x, y) = x/y. Pat’s utility function is U(x, y) = -xy. a. No two of these people have the same preferences. b. They all have the same preferences except for Billy. c. Jim, Jerry, and Pat all have the same...

U= (xy)1/3 Derive the Marshallian demands and indirect utility functions

Given the following utility function U(X,Y)=X0.4 Y0.6 subject to the constraint I=XPx+YPy find: a the marshallian...

Given the following utility function U(X,Y)=X0.4 Y0.6 subject to the constraint I=XPx+YPy find: a the marshallian demand functions for X and Y b the indirect utility function c the expenditure function d the compensated demand functions for X and Y e from 1 and 2 establish whether x and y are inferior or normal goods f discuss the compensating variation, and distinguish it from equivalent variation, for a normal and inferior good. give real life examples

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has an income denoted by I which is devoted to goods X and Y. The prices of goods X and Y are denoted PX and PY. a. Find the consumer’s marginal utility of X (MUX) and marginal utility of Y (MUY). b. Find the consumer’s marginal rate of substitution (MRS). c. Derive the consumer's demand equations for both goods as functions of the variables PX,...

Esther consumes goods X and Y, and her utility function is U(X,Y)=XY+Y For this utility function,...

Esther consumes goods X and Y, and her utility function is U(X,Y)=XY+Y For this utility function, MUX=Y MUY=X+1 a. What is Esther's MRSXY? Y/(X + 1) X/Y (X + 1)/Y X/(Y + 1) b. Suppose her daily income is $20, the price of X is $4 per unit, and the price of Y is $1 per unit. What is her best choice? Instructions: Enter your answers as whole numbers. X = Y = What is Esther's utility when her...

Write the demand functions for the following utility function: U = ln(x) + ln(y)

(a) Find the demand for y in terms of just prices using the utility function U(x,...

(a) Find the demand for y in terms of just prices using the utility function U(x, y) = [x^2 + y^2 ]^1/2 . (b) Is y an inferior or normal good? (c) Are x and y substitutes or complements? (d) Let Px = 1 and Py = 2. What is the price elasticity of demand for y at equilibrium? (e) Find the cross price elasticity of demand for y. (Hint: Use Px as your cross price.)

Your utility function over x and y is U ( x , y ) = l...

Your utility function over x and y is U ( x , y ) = l n ( x ) + 0.25 y. Your income is $20. You don’t know the prices of x or y so leave them as variables (p x and p y). a) (8 points) Find x*, your demand function for x. Find y*, your demand function for y. b) (10 points) Find the cross-price elasticity of demand for x (E x ∗ , p y:...

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