Economics 51D
Due 17 September 2007
PROBLEM SET 3 ANSWERS
1.
The Pinkies of Paramus?
C.
We’ll start with C first, since (hopefully) it’s obvious that the demand curve here is a linear
function.
But the function has Q as a function of P, whereas our supply n demand model has P
on the vertical axis and Q on the horizontal axis—in other words, P as a function of Q.
That’s
easily changed, if we solve for P:
P = 300 – Q / 50.
So if we graph this on our usual Q-P space
(with P on the vertical axis), then the y-intercept is 300 and the slope is – 1 / 50 or -.02.
This
makes sense since we think demand curves are downward sloping.
A.
The size of the market really asks what the maximum potential demand for the good is—we
can find this from our demand curve by putting in 0 for P and seeing how many pinkie rings
would be demanded if we effectively gave them away—15,000.
B.
The answer to Part C above helps us see what the maximum price is that the consumers are
willing to pay.
If we take the equation from Part A and insert Q = 0, then P = 300, or y-intercept.
This actually says that if the price of pinkie rings rises to $300, demand vanishes so that $300 is
effectively the maximum price that someone would pay (technically, it’s $299.99 or $300 – ε,
but we’ll round to $300).
Note that we’ve inferred a bunch of information very quickly and easily from this linear demand
curve.
They are easy to work with and have nice characteristics, like the maximum price and
maximum market size.
D.
If the price of a pinkie ring is $195, then the quantity demanded, using the first demand curve
Q = 15,000 – 50P, is 15,000 – 50*195 = 15,000 – 9,750 = 5,250 pinkie rings.
Similarly, quantity demanded when price is $220 is given by 15,000 – 50*230 = 15,000 – 11,500
= 3,500.
So the quantity demanded declines from 5,250 rings to 3,500 rings.
E.
This is given on the attached spreadsheet.
F.
This is also given on the spreadsheet.
Note that the Total Revenue curve is for the market,
not for an individual firm.
Remember that an individual firm takes the price as given, so its total
revenue would simply be a line through the origin with slope equal to the market price of pinkie
rings.
Nonetheless, it’s interesting to examine how price and quantity interact at the market level
to produce the total revenue function for the market.
As the graph shows, this function looks like
a quadratic function, with a maximum at some intermediate price.
G.
Now we have a very different demand curve.
As we did in Part C, let’s rewrite this function
so that price is the y-axis variable:
P = 900,000 / Q.
Unlike the linear demand curve, there is no
“maximum” price that consumers are willing to pay or any limit to the size of the market—if we