Answer to Question #167685 in Microeconomics for Mohammed Daniz

Question

Let consider one commodity economy is characterized by following demand and supply 

function such that

Qd = a – bp (a, b > 0)

Qs = -c + dp (c, d > 0)

a. Find out the equilibrium price level and output for the commodity.

b. Show mathematically,whathappen to price and output if demand for and supply of the 

product changes.

Use suitable diagrams to show the comparative static analysis.

Answer 1

a. equilibrium price $p*$ is achieved when

Q_s=Q_d

$a-bp=-c+dp$

$dp+bp=a+c$

$p(d+p)=a+c$

$P=\frac{a+c}{d+p}$

substituting the value of P into Q_s gives the equilibrium quantity

Q=$-c+d(\frac{a+c}{d+p})$

b. from the equilibrium condition from above, moving the expression on the left to the right so

that Q_d - Q_s=0:

F= $a-bp+c-dp=0$

$\frac{\delta{F}}{\delta{P}}=-b-d=-(b+d)>0$