Question

This question will ask you to solve for the equilibrium price and quantity as the market experiences two consecutive shocks. The market begins at t=0, with supply and demand described by the equations below. In each subsequent time period, a new shock is experienced, and the market moves to the new equilibrium point. You should model the two shocks described below as consecutive shocks, beginning from the initial time period.

Consider the following system of supply and demand in time period t=0:

Q 0 D = 52 − 2 P 0 D

Q 0 S = P 0 S − 23

In time period t=1, the market experiences a positive supply shock:

Q 1 S = Q 0 S + 15

In time period t=2, the market experiences a positive demand shock:

P 2 D = P 1 D + 6

2.1: What is P* at t=0.

2.2: What is Q* at t=0.

2.3: What is P* at t=1.

2.4: What is Q* at t=1.

2.5: What is P* at t=2.

2.6: What is Q* at t=2.

Answer 1

2.1.

Q_D = 52 - 2P_D

Q_{S =} P_S - 23

Equating the equations, we get equilibrium Price (P*),

52 - 2P = P - 23

P* = 25

2.2.

Placing the value of P* in any of the above equation we get,

Q = 52 - 2(25)

Q* = 2

2.3.

Q1s= Q_s + 15 = P - 23 +15 = P - 8

Q_D = 52 - 2P

Equating the two equations, we get,

P - 8 = 52 - 2P

P** = 20

2.4.

Placing the value of P** in any of the above equation we get,

Q** = 20 - 8

Q** = 12

2.5.

P_1D = P_D + 6 = 52 - 2P + 6 = 58 - 2P

Q1s= P - 8

Equating the two we gwt,

58 - 2P = P - 8

P*** = 22

2.6.

Putting the value of P*** in any equation above, we get

Q*** = 22 - 8

Q*** = 14