**2016 AP Microeconomics Exam FRQ#2**

**(A) What is Martha’s marginal benefit of the fifth unit of good X?**

At a
quantity of 0, we haven’t purchased any units so there is no marginal benefit.

As we
purchase from 0 quantity to the first unit of X, we gain a marginal benefit of
$16.

As we
purchase from the first to the second unit of X, we gain a marginal benefit of
$12.

As we
purchase from the second to the third unit of X, we gain a marginal benefit of
$8.

As we
purchase from the third to the fourth unit of X, we gain a marginal benefit of
$4.

As we
purchase from the fourth to the

**fifth unit**of X, we gain a**marginal benefit of $1**.
Think of

__marginal__as meaning the next purchase. Obviously we can only purchase full units, so when we have 4 units purchased our next marginal purchase is the 5^{th}one and we receive a marginal benefit of $1 from the additional/marginal purchase of that 5^{th}unit.**(B) Calculate the total consumer surplus if Martha consumes 5 units of X. (show your work)**

Remember,
that consumer surplus is the additional value gained from consumption of a good
subtracting what has been paid for that good.

**Answer - Total Consumer Surplus = $12 + $8 + $4 + $0 + $ -3 =**

__$21 of Total Consumer Surplus__
·
Understand that the $4 Cost is also part of the
benefit. Confusing at first, but understand that if I give you $4 for unit X
then unit X is still worth $4, at least to me.

**(C) Martha is currently consuming 4 units of X and 2 units of Y. Use marginal analysis to explain why this combination is not optimal.**

This
combination of Units X and Units Y are not optimal as the marginal benefit
gained from purchasing units X and Y is not equal.

We are use
to seeing these problems as Utility problems and recognizing that the Marginal
Benefits and Marginal Utility formula’s are the same.

**(D) What is Martha’s optimal combination of X & Y?**

1

^{st}– using the formula set the two goods equal by using the formula above. Table is helpful. (:
2

^{nd}– Martha chooses her purchases according to the greatest benefit gained with each purchase.
3

^{rd}– Martha purchases until her income is all spent.**E) Indicate whether each of the following will cause the optimal quantity of good Y to increase, decrease or stay the same.**

**(I) The price of good Y doubles.**

If the
benefit per unit of Y decreases, then we would purchase less of the good. Martha’s first purchase would have been
X as the benefit is 4, which is greater than the benefit of 2.5 for a unit of
Y.

**Answer - The optimal quantity purchased will decrease.**

**(II) Martha’s income falls to $10 with no change in prices.**

If Martha’s
income falls to $10, then she will not be able to purchase 4 units of good Y.

She will
purchase the first 3 units of good X & Y exactly the same way, but then she
has spent $8 and only has $2 left, so she will then only be able to purchase a
unit of Y.

So 1 unit of
X and 3 units of Y will be purchased, this will use all of her income. The
question above asks if the optimal quantity of good Y will decrease, increase,
or stay the same.

Originally
Martha, with $20 of income bought 4 units of good Y, so her purchase of good Y
has decreased.

**Answer – Martha’s purchase of good Y has decreased.**

**(III) Martha’s income doubles and the price of both goods double.**

The answer
to this question should be intuitive in that if Martha’s income doubles and all
goods prices double then Martha is no better off with a doubling of her income
as the ratio of prices to incomes are the same.

3 units of X
at $8 each is $24 spent and 4 units of Y at 4 each is $16 and $24 + $16 = $40

Martha has
spent $40 (all) of her income and bought the same combination of goods X &
Y.

Answer - No
change in optimal combination of goods X & Y.