In this exercise we will work with a linear demand and supply model and explore the properties
of OLS estimators and IV estimators. The two equations will be
Q
d
i = 50 2(Pi + Ti + Ci) + Ui (1)
Q
s
i = 5 + Pi + Vi (2)
where Ui
is independent of Vi
: To help you understand the equation system, you can think of
the Örst equation as the demand curve where Qd
i
is the demand and Pi + Ti + Ci
is the total
price paid by consumers, where Pi
is the sticker price, Ti
is the general sales tax, and Ci
is the
product-speciÖc tax (i.e., cigarettes exercise tax). You can think of the second equation as the
supply curve where Qs
i
is the supply and Pi
is the sticker price. (You may want to ponder upon
the question: why does it make sense to model the demand in terms of the total price while
modeling the supply in term of the sticker price).
1. Solve these two equations to obtain the market price and sales (i.e., let Qd
i = Qs
i = Qi and
then solve for Qi and Pi
in terms of other variables). A student Önds the solution to be
Qi = 20
2
3
(Ti + Ci) + 1
3
(Ui + 2Vi); (3)
Pi = 15
2
3
(Ti + Ci) + 1
3
(Ui Vi): (4)
Do you agree with the above solution
