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

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

Given :-

Demand function, D = 100 - P

Supply function, S = - 30 + 4P

(i)

We know that,

At equilibrium condition,

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

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,

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

Hence,

New equilibrium price will be Rs. 30

$\bold{Equilibrium \: \: Quantity, \: D = \: 100 - P} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ = 100 - 30} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ = 70}$

Hence,

New equilibrium quantity will be 70 units.