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 5th
one and we receive a marginal benefit of $1 from the additional/marginal
purchase of that 5th 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?
1st
– using the formula set the two goods equal by using the formula above. Table
is helpful. (:
2nd
– Martha chooses her purchases according to the greatest benefit gained with
each purchase.
3rd
– 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.
