Question

Assume you have the two markets below:

Market 1

Q_s = 60 + 10P₁   and Q_d = 110 – 60P₁ + 50P₂

Market 2

Q_s = 30 + 15P₂   and Q_d = 60 – 40P₂ +20P₁   

Using an Excel spreadsheet, find the prices for P₁ and P₂ that yield simultaneous market clearing in both markets.

Answer 1

Market 1
Q_s = 60 + 10P₁   and Q_d = 110 – 60P₁ + 50P₂

Market 2
Q_s = 30 + 15P₂   and Q_d = 60 – 40P₂ +20P₁   

_{For market clearing, Qs=Qd}
60 + 10P₁ = 110 – 60P₁ + 50P₂
70P₁ - 50P₂ = 50 ----- 1

30 + 15P₂ = 60 – 40P₂ +20P₁   
20P₁ - 55P₂ = -30 ---- 2

solving 1 and 2, multiplying 2 by 3.5 and subtracting from 1
70P₁ - 50P₂ = 50
70P₁ - 192.5P₂ = -105
192.5P₂ - 50P₂ = 155
142.5P₂ = 155
P₂ = 1.09
70P₁ - 50P₂ = 50
70P₁ = 50 + 5P₂
P₁ = (50 + 54.39)/70 = 1.49

Ax =B
A		X	B
70	-50	P1	50
20	-55	P2	-30
A-1		MINVERSE(A3:B4)
0.02	-0.02
0.01	-0.02
A-1		A		X	A-1		B
0.02	-0.02	70.00	-50.00	P1	0.02	-0.02	50.00
0.01	-0.02	20.00	-55.00	P2	0.01	-0.02	-30.00
1.00	0.00			P1	1.49
0.00	1.00	MMULT(A11:B12,C11:D12)		P2	1.09

Formula used are mentioned, please press ctr+shift+enter after entering the formula and selecting the required number of cells to populate.