Question

suppose the market demand and supply functions are:

D=10-P

S= -1+P

The government implements an excise tax of t=3

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A) What is the supply function under the tax?

B)What are the Equilibrium output and price the consumers pay?

C) What are the consumer surplus and total surplus under the tax?

Answer 1

A) The supply function before tax

S = -1 + P

After the tax, Supply function is

S = -1+(P-tax)

Tax = 3

S = -1 + P - 3

S = -4 + P

The supply function under tax is

S = -4 + P

B) Market is in equilibrium when quantity demanded and quantity supplied become equal

The given demand function is

D = 10 -P

Supply function under tax is

S = -4 +P

When Q = S

10 -P = -4+P

10 +4 = P +P

14 = 2P

P = 14/2 =7

P = 7

Substitute P = 7 in D =10 -P

10 -7 = 3

Equilibrium Output = 3

The price consumers pay = 7

C) Consumer surplus is the difference between maximum price willing to pay and actual market price. It is the area below the demand curve

Producer surplus is the difference between actual market price and minimum price willing to accept. It is the area above supply curve.

Government revenue = tax * quantity

Total surplus = Consumer surplus + producer surplus + tax revenue

* Consumer surplus

The maximum willingness to pay(price when quantity demanded is 0) = 10

Actual price paid by the consumers under tax = 7

The difference between maximum price and actual price = 10 -7 = 3

Equilibrium quantity under tax = 3

Consumer surplus = (1/2) * 3 *3 = 4.5

*​​​​​​ Producer surplus

Under tax, price reveived by producers = 4

The minimum price willing to accept under tax = 1

Difference between actual price and minimum price = 4-1 =3

Producer surplus = (1/2) *3 *3 = 4.5

* Tax revenue = 3 * 3 = 9

Total surplus under tax = 4.5 + 4.5 + 9 =18

Consumer surplus under tax = 4.5

Total surplus under tax = 9