Question

Market 3: Qs = 15 + 7P3 Qd = 25 -2P1 + 3P2 - 4P3

Answer 1

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Solution,

Market Clearing Condition

Qd = Qs

Market 1

$Qs = -5+2P_1\,\,\,\, Qd=15-2P_1-3P_3\\ Qs=Qd\\ -5+2P_1=15-2P_1-3P_3\\ 2P_1+2P_1=15 + 5-3P_3\\ 4P_1=20 - 3P_3 \\P_1=\frac{20 - 3P_3}{4}$

Market 2

$Qs = 6+2P_2\,\,\,\, Qd=30-3P_2-2P_3\\ Qs=Qd \\ 6+2P_2=30-3P_2-2P_3 \\ 2P_2+3P_2=30-6-3P_3 \\ 5P_2=24 - 2P_3 \\P_2=\frac{24 - 4P_3}{5}$

Market 3

20 – 3P3 24 - 4P3 Since, P1 = P2 4 5 20 - 3P3 24 – 4P3 11P3 = 10 - 2 4 5 20 – 3P3 72 – 12P3 11P3 = 10 - + 2 5 100 - (100 – 15P3) + (144 – 24P3) 11P3 10 100 – 100 + 15 P3 + 144 - 24P3 11P3 = 10 110P3 = 144 – 9P3

110P₃ + 9P₃ = 144

P₃ = 144/119 = 1.21

$\\Since,\,P_3 = 1.21 \\P_1=\frac{20 - 3P_3}{4},\, and \,P_2=\frac{24 - 4P_3}{5} \\P_1 =\frac{20 - 3(1.21)}{4} = \frac{20 - 3.63}{4} = \frac{16.37}{4} = 4.09 \\P_2 = \frac{24 - 4(1.21)}{5} = \frac{24 - 4.84}{5} =\frac{19.16}{5} = 3.83$

Price in Market 1 = 4.09

Price in Market 2 = 3.83

Price in Market 3 = 1.21