Question

In: Economics

Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3...

Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3 X square root of bold Y . His budget is $90 per period, the price of X is PX=$2, and the price of Y is PY=$6.

1. Graph the indifference curve when U= 36
2. What is the Tamer’s MRS between goods X and Y at the bundle (X=8 and Y=2 )? What does the value of MRS means? (أحسب القيمة واكتب بالكلمات ماذا تعني القيمة)
3. How much good X and good Y should he buy to maximize his utility?

Solutions

Expert Solution

Budget = $90

PX = $2

PY = $6

Ans1.

Ans2.

1/2 value of MRS means that When Tameer has X=8 and Y=2; he is ready to give up half unit of Y for 1 extra X

Ans3.

How much should he buy to maximize utility?

Solution:

Budget = $90

PX = $2

PY = $6

Lets write the Lagrangian of the optimization Problem:

FONC's will be following:

Using FONCs

Using X=4Y into Budget Equation

Hence optimal X=30 and Y=5

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3...
Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3 X . His budget is $90 per period, the price of X is PX=$2, and the price of Y is PY=$6. 1. Graph the indifference curve when U= 36 2. What is the Tamer’s MRS between goods X and Y at the bundle (X=8 and Y=2 )? What does the value of MRS means? (أحسب القيمة واكتب بالكلمات ماذا تعني القيمة) 3. How much...
Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3...
Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3 X   . His budget is $90 per period, the price of X is PX=$2, and the price of Y is PY=$6. 1. Graph the indifference curve when U= 36 2. What is the Tamer’s MRS between goods X and Y at the bundle (X=8 and Y=2 )? What does the value of MRS means? (أحسب القيمة واكتب بالكلمات ماذا تعني القيمة) 3. How much...
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 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....
a) A consumer derives utility from wealth according to function u(w) = ln w. He is...
a) A consumer derives utility from wealth according to function u(w) = ln w. He is offered the opportunity to bet on the flip of a coin that has the probability pi of coming heads. If he bets $x, he will have w + x if head comes up and w-x if tails comes up. Solve for the optimal x as a function of pi. What is the optimal choice of x when pi = 1/2 ? b) A consumer...
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...
Given the utility function U ( X , Y ) = X 1 3 Y 2...
Given the utility function U ( X , Y ) = X 1 3 Y 2 3, find the absolute value of the MRS when X=10 and Y=24. Round your answer to 4 decimal places.
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...
Harry derives utility from two goods: X and Y . He has an income of 100...
Harry derives utility from two goods: X and Y . He has an income of 100 dollars. Both X and Y cost 2 dollars per unit Given the utility function U = XY (MUx = Y and MUY = X), how many units of X and Y should Harry consume in order to maximize his utility? (a) X = 100, Y = 0 (b) X = 0, Y = 100 (c) X = 50, Y = 50 (d) X =...
Assume a Cobb-douglas utility function of 2 goods x and y given by U = x...
Assume a Cobb-douglas utility function of 2 goods x and y given by U = x 0.5y 0.5 and an initial income I of 100. Let initial price be px = 4 and py = 1. Now vary the price of x from 1 to 7 in steps of 1. So you have 7 prices for x. px = {1, 2, 3, 4, 5, 6, 7} For each of these px, py REMAINS the SAME at 1. In the excel...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT