Solution for Problem Set #1
1. (18pts) Market Demand and Elasticities
: Consider the demand for a Tesla Model S.
Suppose that the demand for a Tesla Model S is Q
d
= 500,000 – 4P + 2P
Maserati
+
25,000P
gas
, where P is the price of big SUVs (in thousands of dollars), P
Maserati
is the
price of a Maserati Ghibli, and P
gas
is the price for a gallon of gasoline. Assume that
supply is given by Q
s
= -10,000 + 5P - 0.2P
Battery
.
P is the price of a lithium battery for
the Tesla Model S.
Assume: P
Maserati
= $100,000; P
gas
= $4/gallon; and P
Battery
=$20,000.
a)
(3pts)What is the equilibrium
price and quantity for a Tesla Model S?
Graph your supply and demand equations in
inverse form (i.e. price on left side of equation and Q on the right) and show the
equilibrium P*, Q*.
Q
d
= 500,000 - 4P + 2P
Maserati
+ 25,000P
Gas
P
Maserati
= $100,000, P
gas
= $4
Q
d
= 500,000 - 4P + 2(100,000)
+ 25000(4)
Q
d
= 800,000 – 4P
Q
s
= -10,000 + 5P - 0.2P
Battery
P
Battery
=$20,000
Q
s
= -10,000 + 5P - 0.2(20,000)
Q
s
= -14,000 + 5P
Inverse Demand Curve
P = 200,000 – (1/4) Q
d
Inverse Supply Curve
P =
2,800+(1/5)Q
s
At equilibrium, S = D
-14,000+5P= 800,000 – 4P
9P=814,000
P*=$90,444
•
Q* = -10,000+5(90,444) or Q*=800,000-4(90,444)
Q* = 438,222