Ecns 300
First Midterm: Answers
Summer 2015
Part A. Definitions:
1. Reservation Price: The maximum (or most) someone is willing to pay for a particular good.
(page 4 of text)
2. Excess Demand: The amount by which quantity demanded exceeds quantity supplied at a given
price that is below the equilibrium price. It is another way of specifying the amount of a
shortage. Another definition is: a situation where quantity demanded exceeds quantity supplied
at a given price that is below the equilibrium price. (page 14)
3. Ad Valorem Tax: A tax levied on a transaction whose amount is based on the money value of
the transaction (as opposed to the number of items transacted). (page 22)
4. Numeraire: A good that is designated to represent “all other goods” so a comparison between a
specific good and “all other goods” can be made. This allows analysis of all goods to be done
using two variables: the good we are analyzing and the Numeraire. The price of the Numeraire
is set a p = 1. In the real world, money serves as a Numeraire in people’s day-to-day
calculations. (see page 26)
5. Indifference Curve: A graphic representation where good 1 is on the horizontal axis and good 2
is on the vertical axis. The indifference curve is the set of points representing different
combinations of goods 1 and 2 for which one receives the exact same enjoyment. Also, you
could have used the very formal definition given in the second paragraph of section 3.3 on page
36 of the text.
6. Marginal Rate of Substitution: The slope of an indifference curve at a particular combination of
goods 1 and 2. In other words, the MRS is the maximum amount of good 2 one is willing to give
up to have one more of good 1. (page 48)
Part B:
1. a. If q = D(p) = 200 – p is the demand for good x
and the supply is fixed at 130, then the
equilibrium price will be where quantity
supplied = quantity demanded: 130 = 200 – p.
Solving for p sets the price at 70. The
equilibrium quantity is 130, and the revenue
to the seller will be 70 x 130 = 9100. This is
graphically represented by the area of
rectangle A in the diagram.
b. If we have a non-discriminating (or “ordinary”)
monopolist, the seller will set a price (and sell
a quantity) that maximizes total revenue. It
was indicated in class that if the demand is a
straight line (as is the case here), the revenue
is maximized at the midpoint on the line between the vertical and horizontal axes. In this
case, that occurs where q = 100 and p = 100. The revenue is 100 x 100 = 10,000.
c. A discriminating monopolist charges the maximum each buyer is willing to pay until all units
are sold. So, there is no single price that is charged (as occurs in the situations described in
parts a and b of this problem), but the maximum quantity is 130 (since that is all the seller
has to supply). The revenue to the seller will be the area under the demand curve up to a
quantity of 130, represented by the combined areas of rectangle A and triangle B in the
diagram. Area of A = 9100 (from part a of this question); the area of B = ½ x 130 x 130 =
8450. The total revenue to the discriminating monopolist is A + B = 17,550.
2. a. The budget equation is $2x1 + $1x2 = $100
b.
c.
d. The budget line for quantities of good 1
between 0 and 20 is not affected by the
tax, so the price of good 1 is $2. But for
amounts greater than 20, there is an excise
tax of $1 added to the price, so the
consumer must pay $3 per unit. This
makes the slope of the budget line change
from -2 for quantities between 0 and 20 to
a slope of -3 for quantities greater than 20.
3. a.
The indifference curves
are straight lines with a
slope = -5
b.
The indifference curves are “L” shaped with the
corners lying on a line that signifies the 3 to 1
ratio that goods 1 and 2 are used in
complementary consumption.
c.
Preference directions change when good 1
becomes a bad.
Part C.
4. See page 45 of your text; bottom paragraph.
5.
a. The budget line is the sold line
in the diagram to the right.
The slope of the first segment
(for quantities of good 1 up to
10) is -4, reflecting that p1 =
$4; the slope of the second
(middle) segment is -2; and
the slope of the third segment
is -1.
b. The dashed line in the diagram
is the budget line if there is a
single price of good 1: p1 = $2.
That budget line has a slope of
-2.
c. Sam would prefer the single
price of $2 per unit because all
points on the dashed budget
line—except for the two end
points on the axes—give Sam
the ability to buy more of
goods 1 and 2 than he can if
he is constrained to the solid budget line.
d. Sellers would generally prefer the solid budget line for a simple reason: they can make more
money. For example, selling the first 10 units for $4 brings in twice as much as selling for $2.
Suppose the seller wants to sell 30 of good 1. Under the “quantity discount” scheme, he will
make $40 on the first 10, and additional $40 on the next 20 for a grand total of $80. On the
other hand, by selling 30 at $2 apiece, he makes $60. (Note that if 50 units are sold, the two
pricing schemes yield the same revenue to the seller of $100.)