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 marginal utility of X ash and the marginal utility of Y ash at the maximum utility?

(2) What is the maximum utility level?

(3) When income is increased from 40 to 80, what is the income elasticity of the demand for X ash?

(4) (While the price of Income 40 and Y ash remains at 1) When the price of X ash falls from 1 to 0.8, find the difference between the maximum utility consumed by price effects and the change in consumption by income effects.

Expert Solution

Rahul Sunny answered 2 years ago

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?

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...

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,...

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....

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 =...

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 = ________

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.

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...

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...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has an income $40 and the price of x is $1 and the price of y is $2. Which bundle will the consumer choose to consume? Determine the demand functions for x and for y. Repeat the exercise if, instead, the consumer’s utility function is u(x, y) = min{x, 2y}.

Question