13. The utility function of consumers who spend both their income and buy X and Y...

13. The utility function of consumers who spend both their income and buy X and Y goods was given U=XY. (U is the size of utility, X is the consumption of X material, Y is the consumption of Y goods) The consumer's income is 100, and the prices of X and Y goods are initially 2 and 10. If the price of X material rises from 2 to 8, what is the compensation income for this change (the minimum income that achieves the same utility level as before)?

Solutions

Expert Solution

The optimal bundle is found when we equate, marginal rate of substitution to the slope of the budget line. The compensation Income is 200 in this scenario to maintain the same level of utility. The working is shown below.

Hope this helps. Do hit the thumbs up. Cheers!

Rahul Sunny answered 2 months ago

Next > < Previous

Related Solutions

Imran has $158 to spend on goods x and y. His utility function is given by...

Imran has $158 to spend on goods x and y. His utility function is given by U(x,y)=min{1x,5y}. The unit price of good y is $2. The unit price of good x is initially $1, but then changes to $7. What is the income effect of the price change on the consumption of good x? Enter a numerical value below. You may round to the second decimal if necessary. Include a negative sign if the answer involves a decrease in quantity.

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...

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...

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...

1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40...

1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro. a) What is the marginal utility of good X (MUx) for the consumer? b) What is the marginal utility of good Y (MUy) for the consumer? How do I calculate these?

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...

An individual has the utility function u = min (x, y). His income is $ 12....

An individual has the utility function u = min (x, y). His income is $ 12. Initially, the prices were px = 4 and py = 1, and the individual consumed the basket x = y = 2.4. Then, px increases to $ 6 (py does not change), and the individual now consumes the basket x = y = 1.71. a) Calculate the compensatory variation of this price change. b) Calculate the equivalent variation of this price change. c) On...

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:...

Meghan’s utility function is given byU( x, y) = x yShe has income I =240 and...

Meghan’s utility function is given byU( x, y) = x yShe has income I =240 and faces prices Px = $ 4and Py = $ 4 Find Meghan’s optimal basket given these prices and her income. If the price of x decreases to $ 2 and Meghan’s income is unchanged, what must the price of y rise to in order for her to be exactly as well off as before the change in Px? (Hint: You need to calculate p...

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...

Subjects