Question

In: Economics

3. (25 marks) Consider an individual with utility of the form: U(x,y) = x0.75+5y. The price...

3. Consider an individual with utility of the form: U(x,y) = x0.75+5y. The price of good x is px and the price of good y is ­py. The individual faces a budget constraint of M. The marginal utility associated with good x is MUx=0.75x-0.25. The marginal utility associated with good y is MUy=5.

  1. Find the Marshallian demand functions for the individual.
  2. Characterize the income elasticity of demand, the price elasticity of demand, the cross-price elasticity of demand and explain what each represents. (You do not need to calculate each elasticity, just tell me if it is positive or negative.)
  3. Suppose px=­py=1, determine the size of the individual’s budget (M) necessary to consume a positive quantity of x and y.

Solutions

Expert Solution


Related Solutions

Consider an individual with utility of the form: U(x,y) = xayb where (a+b)=1. The price of...
Consider an individual with utility of the form: U(x,y) = xayb where (a+b)=1. The price of good x is px and the price of good y is ­py. The individual faces a budget constraint of I (or income). A. Find the demand functions for the individual in question. B. Suppose the price of each good increases by a factor of T (therefore the price of good x is (1+T)px and the price of good y is (1+T)py). Prove that the...
PROVIDE EXPLANATION 2. Elmer’s utility function is U(x, y)  minx, 5y. If the price of...
PROVIDE EXPLANATION 2. Elmer’s utility function is U(x, y)  minx, 5y. If the price of x is $25, the price of y is $10, and Elmer chooses to consume 5 units of y, what must Elmer’s income be? a. $1,350 b. $175 c. $775 d. $675 e. There is not enough information to tell.
Suppose that an individual has a utility function of the form U = Y½ where U...
Suppose that an individual has a utility function of the form U = Y½ where U is utility and Y is income.                        a)   Calculate the utility level for Y values of $10,000, $40,000, $90,000, $160,000, and $250,000 and then plot the individual’s total utility function.                         b)   This individual is currently earning $90,000 but has a 50-50 chance of earning either $40,000 or $160,000 in a new job.                               i)   Calculate the expected income and utility from the new...
Welfare Measures Consider a consumer with utility function of the form u(x,y) = √xy. Where x...
Welfare Measures Consider a consumer with utility function of the form u(x,y) = √xy. Where x is the number of hamburgers and y the number of soft drinks. (a) Find the compensated demands. (b) Calculate the Compensated Variation (CV) when the price of soft drinks increase from $1 to $4. (Assume that the utility at the original price level is equal to 2 and the price of hamburgers is equal to $4) (c) Is the consumer better-off or worse-off after...
An individual utility function is given by U(x,y) = x·y1/2. This individual demand equation for x...
An individual utility function is given by U(x,y) = x·y1/2. This individual demand equation for x is a factor a of I/px: x* = a (I/px). In this specific case, factor a is equal to ______. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed.)
Consider the following utility functions: (i) u(x,y) = x2y (ii) u(x,y) = max{x,y} (iii) u(x,y) =...
Consider the following utility functions: (i) u(x,y) = x2y (ii) u(x,y) = max{x,y} (iii) u(x,y) = √x + y (a) For each example, with prices px = 2 and py = 4 find the expenditure minimising bundle to achieve utility level of 10. (b) Verify, in each case, that if you use the expenditure minimizing amount as income and face the same prices, then the expenditure minimizing bundle will maximize your utility.
An individual has the utility function: U(x,y)=xyx = $ spent on educationy = $...
An individual has the utility function: U(x,y)=xyx = $ spent on educationy = $ spent on other goodsThe individual receives a voucher that pays $S for education or a lump-sum subsidy of $S.1. What is the optimal bundle with the voucher?2. What is the optimal bundle with the lump-sum subsidy?3. With which option is she strictly better off?
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.
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 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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT