Question

In: Economics

An agent considers good 1 and good 2 "perfect substitutes" and thus her preferences can be represented by the utility function u (x,y) = 4x + 2 y.

An agent considers good 1 and good 2 "perfect substitutes" and thus her preferences can be represented by the utility function u (x,y) = 4x + 2 y. The agent starts with $10. Use this information to answer the following questions.

(a) What is the slope of this agents indifference curves (i.e. the mrs)? Hint: You do not need to use calculus if you solve for the equation of an indifference in slope-intercept form.

(b) What is the maximum price at which this agent might purchase any good 1? At this price, is it guaranteed that she will purchase some good 1?

(c) If the price of good 1 is $1.50, how much will she purchase? If the price decreases to $1, how much will she purchase?

(d) Sketch this agents individual demand curve and label the price at which it is horizontal and the amount of good 1 at which it stops being horizontal.

Expert Solution

A) MUx=4

MUy=2

Slope of indifference curve= MUx/MUy=4/2=2

B)Py=1

MUy/py=2/1=2

MUx/px=2

4/px=2

Px=4/2=2

So px=2, maximum price of x ,at which it will buy any amount of x.

No, it is not guaranteed, he can also purchase only Y.

C)At px=1.5,

MUx/px=4/1.5=2.66

So per dollar marginal utility of x is higher than y, so he will only x.

X=10/1.5=6.67

At px=1

MUx/px=4/1=4

So per dollar marginal utility of x is higher than y, so he will only x.

X=10/1=10

4)

At price=0, demand curve become horizontal.

At price above 0, demand curve stop being horizontal

Rahul Sunny answered 2 years ago

Dr Pepper’s preferences can be represented by the utility function u(x,y) = x + y where...

Dr Pepper’s preferences can be represented by the utility function u(x,y) = x + y where x is his consumption of Coca Cola (hereafter, referred to as Coke) and y is his consumption of orange juice (hereafter, referred to as OJ). Initially, both types of drinks are not taxed and with an income of $12 he faces prices ($1, $2). On the advice of nutritionists, the government decides to impose a specific tax of $2 on Coke which leads to...

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.

A consumer's preferences for food (x) and clothes (y) are represented by the utility function u(x,y)=...

A consumer's preferences for food (x) and clothes (y) are represented by the utility function u(x,y)= x + 2 ln(y). The prices of food and clothes are px and py euros/unit, respectively, and the consumer's income is I euros. A. (10 points) Describe the consumer's problem, including her budget constraints, and calculate her ordinary demand functions, x(px,py,I) and y(px,py,I). B. (10 points) For prices and income (px,py,I)=(1,1,3), calculate the substitution and income effects over the demand of y of a...

Judy's preferences over x and y can be represented by the utility function: U=xy3 The price...

Judy's preferences over x and y can be represented by the utility function: U=xy3 The price of x is Px = 8, the price of y is Py = 4, and her income is I = 480. At Judy's optimal consumption bundle, What is her demand for x? What is her demand for y?

"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...

Consider a consumer with preferences represented by the utility function: u(x, y) = x1/4y1/2 Suppose the...

Consider a consumer with preferences represented by the utility function: u(x, y) = x1/4y1/2 Suppose the consumer has income M = 10 and the prices are px=1 and Py = 2. (a) Are goods x and y both desirable? (b) Are there implications for the utility maximization problem for the consumer from your finding in 1a? If so, explain in detail. (c) Derive the utility maximizing bundle.

Consider a consumer with preferences represented by the utility function: u(x; y) = x1/4y1/2 Suppose the...

Consider a consumer with preferences represented by the utility function: u(x; y) = x1/4y1/2 Suppose the consumer has income M = 10 and the prices are px = 1 and py = 2. (a) Are goods x and y both desirable? (b) Are there implications for the utility maximization problem for the consumer from your finding in a? If so, explain in detail.

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.

A consumer has his preferences represented by the utility function U(x,y) = min {5x + 4y,...

A consumer has his preferences represented by the utility function U(x,y) = min {5x + 4y, 4x + 7y} if x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (10,10) a. -4/7 b. -5/4 c. -4/5 d. -7/4 e. -5/7

Suppose a consumer has preferences represented by the utility function U(X,Y) = X2Y Suppose PY =...

Suppose a consumer has preferences represented by the utility function U(X,Y) = X2Y Suppose PY = 1, and the consumer has $300 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...