Question

A market consists of three consumers whose demand curves are: P= 35-0.5Qa; P= 50-0.25Qb; and P= 40-2Qc. Calculate the market demand for the commodity and the equilibrium output and price if the supply function is given by Qs= 40+3.5P. (8 marks)

Answer 1

$Qa=\frac{P-35}{-0.5}$

$Qb=\frac{P-50}{-0.25}$

$Qc=\frac{P-40}{-2}$

$Qs=Qa+Qb+Qc$

$\frac{P-35}{-0.5}+\frac{P-50}{-0.25}+\frac{P-40}{-2}=40+3.5P$

$4(P-35)+8(P-50)+P-40=-80-7P$

$20P=500$

$P=25$

$Qs=87.5$