Question

The demand and supply funtion of the firm under perfectly competitive market is d=100-p and s=-30+4p then find out the equilibrium level of price and output and if the gvrt inposes a tax of rs5 on each unit of output , find out the impact on equilibrium level ofprice and output​

Answer 1

Answer:

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∣SOLUTION∣

Given :-

Demand function, D = 100 - P

Supply function, S = - 30 + 4P

(i)

We know that,

At equilibrium condition,

\begin{gathered} \: \: \: \: \bold{Demand = Supply} \\ \\ \bold{= > 100 - P = - 30 + 4P} \\ \\ \bold{= > - P - 4P = - 30 - 100} \\ \\ \bold{= > - 5P = - 130} \\ \\ \bold{ = > P = \frac{ - 130}{ - 5} } \\ \\ \: \: \: \: \bold{ \therefore \: \: P = 26}\end{gathered}

Demand=Supply

=>100−P=−30+4P

=>−P−4P=−30−100

=>−5P=−130

=>P=

−5

−130

∴P=26

Hence,

Equlibrium Price = Rs. 26.

(ii)

If the govt. impose a tax of Rs. 5 , then

New supply will be ,

S = - 30 + 4( P - 5 )

=> S = - 30 + 4P - 20

=> S = - 50 + 4P

Demand will be the same, i.e., D = 100 - P

So,

At new equlibrium,

\begin{gathered} \: \: \: \: \bold{Demand = Supply} \\ \\ \bold{= > 100 - P = - 50 + 4P} \\ \\ \bold{= > - P - 4P = - 50 - 100} \\ \\ \bold{= > - 5P = - 150} \\ \\ \bold{ = > P = \frac{ - 150}{ - 5} } \\ \\ \: \: \: \: \bold{ \therefore \: \: P = 30}\end{gathered}

Demand=Supply

=>100−P=−50+4P

=>−P−4P=−50−100

=>−5P=−150

=>P=

−5

−150

∴P=30

Hence,

New equilibrium price will be Rs. 30

\begin{gathered} \bold{Equilibrium \: \: Quantity, \: D = \: 100 - P} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ = 100 - 30} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ = 70}\end{gathered}

EquilibriumQuantity,D=100−P

=100−30

=70

Hence,

New equilibrium quantity will be 70 units.

Explanation:

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