Suppose that there are two goods, X and Y. The utility function is ?(?, ?) =...

Suppose that there are two goods, X and Y. The utility function is ?(?, ?) = 5?² ?. The price of Y is $2 per unit, and the price of X is P. Income is $2,400.

A.) Derive the demand curve and state the law of demand in relation to your product or service.

B.) ? = 800 − 10?^0.5 . Calculate elasticity of demand when Q=100, Is the good elastic?

C.) ? = 800 − 10?^0.5 − 0.5?. Calculate elasticity of income when Q=4 and I=100. Is the good normal or inferior?

D.) ?_A = 80 − 10?^0.5 − ?B Calculate cross price elasticity when Q= 16 and ?B =10. Are the goods complementary or are they substitutes?

Expert Solution

Rahul Sunny answered 2 years ago

Suppose that there are two goods, X and Y. The utility function is ?(?, ?) =...

Suppose that there are two goods, X and Y. The utility function is ?(?, ?) = 5?2 ?. The price of Y is $2 per unit, and the price of X is P. Income is $2,400. A.) Derive the demand curve and state the law of demand in relation to your product or service. B.) ? = 800 − 10?0.5 . Calculate elasticity of demand when Q=100, Is the good elastic? C.) ? = 800 − 10?0.5 − 0.5?. Calculate...

A consumes two goods, x and y. A ’s utility function is given by u(x, y)...

A consumes two goods, x and y. A ’s utility function is given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of y is 1. A has an income of M. (a) Derive A ’s demand functions for x and y. (b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution effects of the price change. (c) Calculate the compensating variation of the price change....

For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)=...

For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)= ?0.5?0.5, the price of good y is $10, income equals $100, and the price of good x increase from $5 to $10. Draw the price consumption curve for x and y and compute the slop of the price consumption curve. Show your calculation step by step.

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...

A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...

A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x) + 3y. For this utility function MUx =1/x and MUy = 3. The price of x is px = 4 and the price of y is py = 2. The consumer has M units of income to spend on the two goods and wishes to maximize utility, given the budget. Draw the budget line for this consumer when M=50 and the budget line when...

13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y)...

13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of y is 1. Pip has an income of M. (a) Derive Pip’s demand functions for x and y. [5 marks] (b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution effects of the price change. [5 marks] (c) Calculate the compensating variation of...

Leon consumes two goods, X and Y. His utility function is given by U(X,Y) = 56XY....

Leon consumes two goods, X and Y. His utility function is given by U(X,Y) = 56XY. The price of X is $14 a unit; the price of Y is $8 a unit; and Leon has $672 to spend on X and Y. a. Provide the equation for Leon’s budget line. (Your answer for the budget line should be in the form Y = a – bX, with specific numerical values given for a and b.) b. Provide the numerical value...

Ron consumes two goods, X and Y. His utility function is given by U(X,Y) = 33XY....

Ron consumes two goods, X and Y. His utility function is given by U(X,Y) = 33XY. The price of X is $11 a unit; the price of Y is $4 a unit; and Ron has $352 to spend on X and Y. a. Provide the equation for Ron’s budget line. (Your answer for the budget line should be in the form Y = a – bX, with specific numerical values given for a and b.) b. Provide the numerical value...

cosnider the following utility fucntions over goods X and Y for two indiviuals: jills utility function...

cosnider the following utility fucntions over goods X and Y for two indiviuals: jills utility function is Uj(x,y) = 6min(X,Y) bob's utility function Ue(x,y) = 6x + 3y A) for Janet, draw her indifference curve map for two specific utility levels: Utility = 6 and utility = 12. indicate key value of X and Y on the proper axis. label the indifference curves U=6 and U=12.

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x and y are the quantities of the good X and good Y consumed, respectively. The consumer's income is 400. (a) What is the demanded bundle when the price of good X is 10 and the price of good Y is 10? (b) Redo part (a) when the price of good X is doubled? (c) Redo part (a) when the price of good Y is...

Question

Suppose that there are two goods, X and Y. The utility function is ?(?, ?) =...

Solutions

Expert Solution

Related Solutions

Suppose that there are two goods, X and Y. The utility function is ?(?, ?) =...

A consumes two goods, x and y. A ’s utility function is given by u(x, y)...

For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)=...

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

A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...

13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y)...

Leon consumes two goods, X and Y. His utility function is given by U(X,Y) = 56XY....

Ron consumes two goods, X and Y. His utility function is given by U(X,Y) = 33XY....

cosnider the following utility fucntions over goods X and Y for two indiviuals: jills utility function...

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...