Question

Calculate the equilibrium price and quantity for the following functions

Qd1= -7p1 + 2p2 +19

Qd1= 4p1-5

Qd2= 4p1-4p2 +10

Qs2= 8p2-4



Solve by using inverse method and Cramer's rule

Answer 1

$Qd_1=Qd_1\\4P_1-5=-7P_1+2P_2+19\\4P_1+7P_1-5-19=2P_2\\\frac{11P_1}{2}-\frac{24}{2}=2P_2\\\frac{11P_1}{2}-12=P_2$

$Qd=Qs\\4P_1-4P_2+10=8P_2-4\\10+4=8P_2-4P_1+4P_2\\14=12P_2-4P_1\\\frac{12P_2}{12}=\frac{14}{12}+\frac{4P_1}{12}\\P_2=\frac{14}{2}+\frac{4}{12}P_1$

$\frac{14}{12}+\frac{4}{12}P_1=\frac{11}{2}P_1-12$

$\frac{14}{12}+12=\frac{11}{2}P_1-\frac{14}{12}P_1$

$\frac{13.167}{5.167}=P_1\\P_1=2.548$

$Q_1=4P_1-5\\=4(2.548)-5\\=5.192\\$

$P_2=\frac{1}{2}P_1-12$

$\frac{11}{2}\times2.548-12\\=2.014$

$Q_2=8P_2-4\\=8\times2.014-4\\=12.112$