At equilibrium price, the quantity demanded is equal to quantity supplied in the market
Qd=Qs
therefore
(a−bp)=(c+dp)
(a−c)=(dp+bp)
(a−c)=p(d+p)
p=(a−c)/(b+d)
equilibriumprice=(a−c)/(b+d)
Equilibrium quantity is gotten by substituting the equilibrium price into the demand equation
Qd=a−bp
qd=a−b[b+da−c]
q=a−[b+dab+cb]
Q=b+d(ab+bd)−(ab+cb)
Q=b+dab−ab+cb+bd
EQUILLIBRIUM QUANTITY IS GIVEN BY
Q=b+dcb+ad
Price elasticity of demand at equilibrium
priceelasticity=percentagechangeinpricepercentagechangeinquantity
PERCENTAGE CHANGE IN QUANTINTY =QΔQ
PERCENTAGE CHANGE IN PRICE=PΔP
change in quantityΔQ=Q1−Q
change in priceΔQ=P1−P
PRICE ELASTICITY =QΔQ×ΔPP
PRICE ELASTICITY =ΔPΔQ×QP
but from the demand equation ΔPΔQ is the gradient of the equation
therefore from Qs=(a−bp) −b is the gradient of the equation
the price elasticity of demand will be
Pe=−b×qP
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