Question

Consider an economy described by the following equations:

QD = 30M - 2P

QS = (1-t)P -5

QD = QS

where QD is quantity demanded, QS is quantity supplied, M is the income of consumers, and t is the tax rate (with 0 < t < 1). Consider the vector of endogenous variables X = [ QD P QS ] T .

1)Write the model in matrix form.

2) Does the model have a unique solution? Explain.

3) Solve the model by matrix inversion. (You have to show the work done to calculate the inverse! “Magical” inverse matrices will not be accepted.)

4) Find the equilibrium value of P by using Cramer's rule. Check whether you obtain the same solution as the one from question 3.

5) Suppose you want to find out the tax rate, income and price in an equilibrium with QD = QS = 7. How would you change your answer to question 1?

Answer 1

Subject to do only 4 parts.

Hint for 5th:-- just now the X vector will change

Now the X = [ t M P ]^T

Now do same as the below.