Question

Suppose Suzuki has the following demand and supply function for Cultus VXL: Qd = 55 - 5P Qs = -50 + 10P After the government decided to impose tax on the production of Cultus VXL, the new supply function: Qs = -60 + 10P Given the information above answer the following questions: Find out the equilibrium price and quantity before tax. Find consumer and producer surplus before tax. Determine government revenue and dead weight loss after tax.

Answer 1

Answer:

Explanation:

From the information given:

The equilibrium price before tax creates an intersection between the demand and supply.

Qd = 55 -5 P    Qs = -50 + 10 P

i.e.

55 - 5P = -50 + 10P

55 + 50 = -5P +10P

110 = 5P

P = 110 / 5

P' = 7

replacing the value of P into the demand equation; we have

Qd = 55 - 5P

Qd = 55 - 5(7)

Qd = 55 - 35

Q' = 20

This tells us that the equilibrium quantity = 20 prior to the equilibrium price which is 7 before tax.

Consumer Surplus = $\dfrac{1}{2} Q' \times (P-P')$

= $\dfrac{1}{2}\times 20 \times (11 -7)$        (∵ if P is the intercept of the demand and Q is set to be 0, P =11)

Consumer Surplus = 40

Producer surplus = $\dfrac{1}{2}Q^*(P^*-P')$

here;

P' = y-intercept of supply curve = 5 since we set Qs to be 0

$=\dfrac{1}{2}\times 20 \times (7-5)$

Producer surplus = 20

Thus prior to commencement of the tax consumer surplus and producer surplus are 40 and 20 respectively.

After-tax:

Qd = 55 - 5p      Qs = -60 + 10 P

55 -5 P = -60 + 10 P

115 = 15P

P** = 23/3

Replacing this into the demand

Qd = 55 - 5P

Qd = 55 - 5(23/3)

Qd = 50/3

Thus, after-tax equilibrium quantity = 50/3 and equilibrium pric = 23/3.

Government revenue = (Tax)Q**

Here;

Q** = (P** - P'')

i.e.

P**  = after tax equilibrium price

P'' = price suppliers received when Q** is determined in the previous supply curve =20/3

Government Tax revenue = (23/3 - 20/3) × 50/3

Government Tax revenue = 50/3

Dead weight loss = 1/2 × Tax × (Q* - Q**)

Dead weight loss  $=\dfrac{1}{2} * (\dfrac{23}{3} -\dfrac{20}{3}) * (20 -\dfrac{250}{3})$

Dead weight loss  = 5/3