Question

In: Economics

Leo's utility function is U=min(6x,2y). If Leo's income is 6 dollars, the price of good X...

Leo's utility function is U=min(6x,2y). If Leo's income is 6 dollars, the price of good X is 8 and the price of good Y is 7, how many units of good X will Leo buy in order to maximize his utility?

Solutions

Expert Solution

Preferences are perfect Complements

Two goods are consumed in fixed proportions

6x =2y

3x = y

From BC : 8x + 7y = 6

Put y = 3x

So, 8x + 21x = 6

29x = 6

x* = 6/29


Related Solutions

A consumer has a utility function of U = min{4x1, x2}. The price of good 1...
A consumer has a utility function of U = min{4x1, x2}. The price of good 1 is $8 and the price of good 2 is $5. The consumer has $112 in income. How many units of each good does she consume? x1 = 8, x2 = 8 x1 = 16, x2 = 4 x1 = 12, x2 = 8 x1 = 4, x2 = 16 None of the above Consider the inter-temporal model of consumption studied in class, with two...
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...
Amy has the utility function U=min(2x+y, x+2y) for goods x and y. 1) Draw the indifference...
Amy has the utility function U=min(2x+y, x+2y) for goods x and y. 1) Draw the indifference curves where U=6 and U=12. 2) Draw Amy's typical demand curve for good x.
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.
Consider the following five utility functions. G(x,y) = -1 / [ min(6x,2y)+1] H(x,y) = min(6x,6y)2 L(x,y)...
Consider the following five utility functions. G(x,y) = -1 / [ min(6x,2y)+1] H(x,y) = min(6x,6y)2 L(x,y) = min(6x,2y) - 10000000000 U(x,y) = min(3x, y)3 W(x,y) = min (6x, y)2 + 2 Z(x,y) = min (x,2y) Which of the above functions, if any, is homogeneous of degree 2? a. L b.W c.Z d.None. e.H f.G g.U
Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the...
Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the price of good p2, the income is y. a. Derive ordinary demand functions. b. Draw indifference curves and budget line for the case when the price of good 1 is 10, the price of good 2 is 20, the income is 1200. c. Find the optimal consumption bundle.
Ella’s preferences can be represented by the utility function u(x,y) = min{5x, y}. If the price...
Ella’s preferences can be represented by the utility function u(x,y) = min{5x, y}. If the price of x is $10 and the price of y is $15, how much money would she need to be able to purchase a bundle that she likes as well as the bundle (10, 25). Select one: a. $475. b. $85. c. $425. d. $209. e. $440.
Jane’s utility function is U(x, y) = x + 2y, where x is her consumption of...
Jane’s utility function is U(x, y) = x + 2y, where x is her consumption of good X and y is her consumption of good Y. Her income is $2. The price of Y is $2. The cost per unit of X depends on how many units she buys. The total cost of x units of X is the square root of x. The bundle ( 1 4, 3 4 ) is Jane’ s utility maximizing choice, given her budget....
For one purpose, the utility function of the consumer is u(x,y)=4?x+2y for maximum utility. 1. For...
For one purpose, the utility function of the consumer is u(x,y)=4?x+2y for maximum utility. 1. For one purpose, the customer's income is I, and the price of X is Px and the price of Y is Py. Obtain the demand function of this person's Y ash through Px, Py, I. 2. For one purpose, the consumer has an income I = 40, and initially the price of Px=1, and the price is Py=1. (1) What is the difference between the...
Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of...
Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of px = 1 and py = 2. Assuming that graphically good x is on the horizontal axis and good y is on the vertical axis, suppose the consumer chooses to consume 5 units of good x and 13 units of good y. What is the marginal rate of substitution (MRS) equal to?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT