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