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.

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 =

=        (∵ if P is the intercept of the demand and Q is set to be 0, P =11)

Consumer Surplus = 40

Producer surplus =

here;

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

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  

Dead weight loss  = 5/3

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.

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