The market supply and demand function are as follows:
Qd =1200-2P
Qs = 4P
On the basis of this information, answer the following:
a) Determine the equilibrium price and quantity
b) What is the effect of tax Rs 50 per unit on production?
Solution:
In the above question, the demand function is :
Qd =1200-2P
Similarly, the supply function is :
Qs = 4P
a) Computation of equilibrium price and quantity
As we know, at equilibrium point the market demand equals market supply.
In other words,
Qd = Qs
Putting the values of Qd and Qs
1200-2P = 4P
6P = 1200
Or, P = Rs.200
Now, putting the value of P in demand function
Qd = 1200 – 2p = 1200 -2 x 200 = 800 unit.
Similarly, putting the value of P in supply function
Qs = 4P = 4 X 200 = 800 unit.
Therefore, the required equilibrium price and quantity is Rs. 200 and 800 units respectively.
b) Computation of Effect due to tax of Rs 50 per unit on production:
Since, the effect of tax do not affect the market demand function but affects the market supply function, we need to first compute the new market supply function by considering the effect of tax.
Market Demand Function:
Qd = 1200 – 2P
Market Supply Function:
Qs = 4 (P – 50 )
Or Qs = 4P – 200
Again, at Market Equilibrium Point
Qd = Qs
Putting the values of Qd and Qs
1200-2P = 4P – 200
Or, 6P = 1400
Or, P = Rs. 233.33
Now, Putting the value of P in demand function
Qd = 1200 – 2p = 1200 -2 x 233.33 = 733.33 = 733 unit
Similarly, putting the value of P in supply function
Qs = 4P – 200 = 4 X 233.33 – 200 = 733.33 = 733 unit
Therefore, the new equilibrium price and quantity is Rs. 200 and 800 units respectively.
Qd =1200-2P
Similarly, the supply function is :
Qs = 4P
a) Computation of equilibrium price and quantity
As we know, at equilibrium point the market demand equals market supply.
In other words,
Qd = Qs
Putting the values of Qd and Qs
1200-2P = 4P
6P = 1200
Or, P = Rs.200
Now, putting the value of P in demand function
Qd = 1200 – 2p = 1200 -2 x 200 = 800 unit.
Similarly, putting the value of P in supply function
Qs = 4P = 4 X 200 = 800 unit.
Therefore, the required equilibrium price and quantity is Rs. 200 and 800 units respectively.
b) Computation of Effect due to tax of Rs 50 per unit on production:
Since, the effect of tax do not affect the market demand function but affects the market supply function, we need to first compute the new market supply function by considering the effect of tax.
Market Demand Function:
Qd = 1200 – 2P
Market Supply Function:
Qs = 4 (P – 50 )
Or Qs = 4P – 200
Again, at Market Equilibrium Point
Qd = Qs
Putting the values of Qd and Qs
1200-2P = 4P – 200
Or, 6P = 1400
Or, P = Rs. 233.33
Now, Putting the value of P in demand function
Qd = 1200 – 2p = 1200 -2 x 233.33 = 733.33 = 733 unit
Similarly, putting the value of P in supply function
Qs = 4P – 200 = 4 X 233.33 – 200 = 733.33 = 733 unit
Therefore, the new equilibrium price and quantity is Rs. 200 and 800 units respectively.
Effect before tax
|
Effect after tax
|
|
Price
|
Rs. 200
|
Rs. 233.33
|
Quantity
|
800 Unit
|
733 unit
|
The effect of tax is that, it increases the price and decreases the quantity.
Tutorial Note :
If there would be subsidy in the question then, add the government subsidy in the supply function and solve the problem accordingly. Subsidy decreases price and increases quantity.
