Question

In: Economics

Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...

Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y − 3.5)^2 Further assume that the price of good x, px = $6, the price of good y, py = $8, and the individual has an income m = $65

a) Draw an indifference curve (one IC is enough) that represents this person’s preferences. Please label the graph properly including values for x and y.

b) Intuitively, and without formally solving, can you guess the maximized values x* and y* for the above utility function. Explain your answer.

c) Derive the optimal values x*and y* by formally solving the above utility function subject to the above constraint. You can use any of the utility maximization techniques we learned in class.

d) Compare your answers in parts b) and c). Based on the utility function that is given in this problem as well as the budget constraint, can you explain the differences between the answers

Solutions

Expert Solution


Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y − 3.5)^2 Further assume that the price of good x, px = $6, the price of good y, py = $8, and the individual has an income m = $65 a) Draw an indifference curve (one IC is enough) that represents this person’s preferences. Please label the graph properly including values for x and y. b) Intuitively, and without formally solving, can you guess...
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y − 3.5)^2 Further assume that the price of good x, px = $6, the price of good y, py = $8, and the individual has an income m = $65 a) Draw an indifference curve (one IC is enough) that represents this person’s preferences. Please label the graph properly including values for x and y. b) Intuitively, and without formally solving, can you guess...
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...
Suppose an individual has the following utility function: U(X,Y) = 2XY. Draw the budget constraint when...
Suppose an individual has the following utility function: U(X,Y) = 2XY. Draw the budget constraint when the price of each unit of X and Y are 5 and 4, and income is 120. Find the choice that maximizes utility.
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.)
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?
"Suppose a consumer has preferences represented by the utility function U(X,Y) = X(^2)Y Suppose Py =...
"Suppose a consumer has preferences represented by the utility function U(X,Y) = X(^2)Y Suppose Py = 1, and the consumer has $360 to spend. Draw the Price-Consumption Curve for this consumer for income values Px =1, Px = 2, and Px = 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also for each bundle that the consumer chooses, draw the indifference curve...
Suppose a consumer has a utility function given by u(x, y) = x + y, so...
Suppose a consumer has a utility function given by u(x, y) = x + y, so that the two goods are perfect substitutes. Use the Lagrangian method to fully characterize the solution to max(x,y) u(x, y) s.t. x + py ≤ m, x ≥ 0, y ≥ 0, where m > 0 and p < 1. Evaluate and interpret each of the multipliers in this case. What happens to your solution when p > 1? What about when p =...
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...
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,...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT