Question

In: Economics

Consider the following utility function: U = 100X0.10 Y 0.75. A consumer faces prices of Px...

Consider the following utility function:

U = 100X0.10 Y 0.75.

A consumer faces prices of Px = $5 and Py =$5.
Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer

chooses to consume 7 units of good X and 15 units of good Y. Then the marginal rate of substitution6 is equal to:
MRS = . (Enter your response rounded to two decimal places. Do not forget to include the negative

sign.)
Use absolute values.

The consumer should consume (1) to maximize utility.

Solutions

Expert Solution


Related Solutions

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?
Let assume that a consumer has a utility function u(x, y) = xy, and px =...
Let assume that a consumer has a utility function u(x, y) = xy, and px = 1 dollar, py = 2 dollars and budget=50. Derive the followings. (3 points each) 1) Marshallian demands of x and y 2) Hicksian demands of x and y 3) Indirect utility function 4) Expenditure function 5) Engel curve
a consumer has a utility function u = x^1/2y^1/2. prices are px = 2 and py...
a consumer has a utility function u = x^1/2y^1/2. prices are px = 2 and py = 3. she maximizes utility purchasing 6 units of good x. her income is equal to m = ________
Consider the following utility function: u(x, y) = x2/3y1/3. Suppose that Px = 4, Py =...
Consider the following utility function: u(x, y) = x2/3y1/3. Suppose that Px = 4, Py = 2 and the income is I = 30. Derive the optimal choice for both goods.
Consider a quasi-linear utility function, U(X, Y) = X1/2 + Y, with some Px and Py...
Consider a quasi-linear utility function, U(X, Y) = X1/2 + Y, with some Px and Py a. For an interior solution, solve step-by-step for the demand functions of X* and Y*. b. Under what circumstance would the optimal consumption involve a corner solution for the utility maximization problem? c. (Now, let Py = $1, I = 24, and suppose that Px increases from $0.5 to $2. Find the Compensating Variation (CV) and the Equivalence Variation (EV). In this example, how...
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,...
Suppose a consumer has preferences represented by the utility function U(X,Y) = MIN[X,2Y]. Suppose PX =...
Suppose a consumer has preferences represented by the utility function U(X,Y) = MIN[X,2Y]. Suppose PX = 1 and PY = 2. Draw the Income Consumption Curve for this consumer for income values M = 100, M = 200, and M = 300. 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 that...
Brianna’s preferences can be represented by the utility function u(x,y) = min{x,y}. Initially she faces prices...
Brianna’s preferences can be represented by the utility function u(x,y) = min{x,y}. Initially she faces prices ($2,$1) and her income is $12. If prices change to ($3,$1) then the compensating variation Select one: a. There is not enough information to determine which variation is greater. b. is $2 more than the equivalent variation. c. is $1 less than the equivalent variation. d. equals the equivalent variation. e. is $1 more than the equivalent variation.
Consider the following utility function U(X,Y) = X^1/4Y^3/4 Initially PX = 2 PY = 4 I...
Consider the following utility function U(X,Y) = X^1/4Y^3/4 Initially PX = 2 PY = 4 I = 120 Suppose the price of X changes to PX = 3. Perform a decomposition and fill in the table X Y Substitution Effect Income Effect Total Effect
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT