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.

Solutions

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

At price=0, demand curve become horizontal.

At price above 0, demand curve stop being horizontal

Rahul Sunny answered 1 year ago

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