Answer to Question #270450 in Economics of Enterprise for Abdi Obsa

Question #270450

Suppose market demand is given Qd=a-bp as and market supply is given as, Qs=c+dp and then find the following



o Equilibrium price



o Equilibrium quantity



o Price elasticity of demand at equilibrium



o Price elasticity of supply at equilibrium

1
Expert's answer
2021-11-24T19:28:35-0500

At equilibrium price, the quantity demanded is equal to quantity supplied in the market

Qd=QsQ{d}=Q{s}

therefore

(abp)=(c+dp)(a- bp)= (c+dp)

(ac)=(dp+bp)(a-c) =(dp + bp)

(ac)=p(d+p)(a - c)=p(d +p)

p=(ac)/(b+d)p=(a - c)/(b + d)

equilibriumprice=(ac)/(b+d)equilibrium price =(a - c)/(b + d)


Equilibrium quantity is gotten by substituting the equilibrium price into the demand equation

Qd=abpQd=a - bp

qd=ab[acb+d]qd =a- b[\frac{ a-c}{b+d}]

q=a[ab+cbb+d]q=a- [\frac{ab +cb}{b+d}]


Q=(ab+bd)(ab+cb)b+dQ =\frac{(ab+bd)-(ab+cb)}{b+d}


Q=abab+cb+bdb+dQ=\frac{ab -ab+cb+bd}{b+d}

EQUILLIBRIUM QUANTITY IS GIVEN BY

Q=cb+adb+dQ=\frac{cb + ad}{b + d}


Price elasticity of demand at equilibrium


priceelasticity=percentagechangeinquantitypercentagechangeinpriceprice elasticity=\frac{percentage change in quantity}{percentagechange in price}


PERCENTAGE CHANGE IN QUANTINTY =ΔQQ\frac {\Delta Q}{Q}

PERCENTAGE CHANGE IN PRICE=ΔPP\frac {\Delta P}{P}

change in quantityΔQ=Q1Q\Delta Q =Q{1}- Q

change in priceΔQ=P1P\Delta Q =P{1}- P


PRICE ELASTICITY =ΔQQ×PΔP\frac{\Delta Q}{ Q} \times \frac{P}{\Delta P}


PRICE ELASTICITY =ΔQΔP×PQ\frac{\Delta Q}{\Delta P } \times \frac{P}{Q}

but from the demand equation ΔQΔP\frac{\Delta Q}{\Delta P } is the gradient of the equation

therefore from Qs=(abp)Q{s}=(a- bp) b-b is the gradient of the equation



the price elasticity of demand will be


Pe=b×PqP{e}=-b \times \frac{P}{q}





Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS