I am trying to calculate the reduction in consumer surplus and producer surplus

caused by the tax in this graph.

The price with the tax is $12. The buyers pay $16. Sellers receive $8. The quantity has decreased from 25 to 15.

The answers provided for the reduction of consumer and producer surplus are $100,$80,$70, $60 for each.

I am getting $60 for each reduction in consumer and producer surplus and it does not seem right to me.
Price $
22_________________
20_________________
18_________________
16_________________
_________{___|_____|
12_______{TAX|_____|
_________{___|_____|
8____________|_____|
6____________|_____|
4____________|_____|
2____________|_____|
______5__10__15_20_25_30_Quantity

As you can see, trying to produce a graph on this Jiskha is an exercise in frustration.

However, based on the facts you gave me, and ASSUMING your supply and demand functions are linear, I can reconstuct your your graph and determine the changes in producer and consumer surplus. Start by drawing linear supply and demand curves, with initial price at 12, Q at 25. After the tax buyers pay 16, sellers get 8. So the tax must be 8. Draw a new supply curve which is, vertically, 8 above the original supply. Label the new price 16, the new Q is 15.

Your graph should have an area representing the change in consumer surplus. Lets break this area into to parts, the first is the rectangular area with height 4 (between the original 12 and the new 16) and length 15. The value of the area of this box is 4*15 = 60. You also have the little triangle, with height 4 and length 10. The area of the triangle is .5*4*10 = 20. So, change in consumer surplus is 80.

Thank you for your assitance. Yes trying to put a graph on Jiskha is not an easy task. I will review what you gave me. I unstand what I was trying to come up with. I thought I did get the correct answer for the concumer surplus. I was not sure of the producer suplus. Any thoughts as to how I could draw a graph if I need to ask a question? I don't think I have any software that I could try to use.

The tax was $8, consumers paid $4 more, producers got $4 less. With linear supply and demand curves, the results must and symetric changes, the changes in producer and consumer surplus must be the same. Change in producer surplus is also 80.

Also, I have no idea how to draw a graph in Jiskha.

In the area of the triangle .5*4*10=20. Where is the .5 coming from?

To calculate the reduction in consumer surplus and producer surplus caused by the tax, we need to compare the situation with the tax to the situation without the tax. Let's break down the steps:

1. Find the equilibrium price and quantity without the tax:
Based on the information provided, the equilibrium price without the tax is $16 and the equilibrium quantity is 25.

2. Calculate consumer surplus without the tax:
Consumer surplus represents the difference between the maximum price buyers are willing to pay and the actual price paid. Without the tax, buyers would have paid $16, which is the equilibrium price. The graph suggests that the demand curve may be linear, so we can calculate consumer surplus as the area of the triangular region between the demand curve and the equilibrium price. The consumer surplus without the tax can be calculated as follows:

Consumer Surplus = 0.5 * (25 - 15) * (16 - 12) = $20

3. Calculate producer surplus without the tax:
Producer surplus represents the difference between the actual price received by sellers and the minimum price they are willing to accept. Without the tax, sellers would have received $16, which is the equilibrium price. The graph suggests that the supply curve may be linear, so we can calculate producer surplus as the area of the triangular region between the supply curve and the equilibrium price. The producer surplus without the tax can be calculated as follows:

Producer Surplus = 0.5 * (25 - 15) * (16 - 8) = $40

4. Calculate the reduction in consumer surplus:
With the tax, the price is $12, and the quantity is 15. To find the reduction in consumer surplus, we need to calculate the new consumer surplus and subtract the original consumer surplus.

Consumer Surplus with Tax = 0.5 * (15 - 0) * (16 - 12) = $30

Reduction in Consumer Surplus = Consumer Surplus without Tax - Consumer Surplus with Tax
= $20 - $30
= -$10

5. Calculate the reduction in producer surplus:
To find the reduction in producer surplus, we need to calculate the new producer surplus and subtract the original producer surplus.

Producer Surplus with Tax = 0.5 * (15 - 0) * (16 - 8) = $30

Reduction in Producer Surplus = Producer Surplus without Tax - Producer Surplus with Tax
= $40 - $30
= $10

Based on the calculations, the reduction in consumer surplus is -$10 and the reduction in producer surplus is $10, not $60 as you mentioned before. It seems there may have been an error in your calculations or understanding of the concept. I hope this explanation clarifies the correct approach to solving the problem.