Economics
posted by G on .
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.

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

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.