2/17/12

Consumer and producer surplus with a change in supply, a question and answer



This article is a question and answer for the economics of consumer and producer surplus.  The following question was presented:

I have an equilibrium chart where supply and demand intersect at 5. The price is 1$ for 1 good. The question is: assume that the cost of producing that good increases by 2$ at every possible quantity. Recalculate the consumer and producer surplus at this new equilibrium and determine if it is efficient.

My original chart has a max height of 10 and max width of 10. The supply and demand curves intersect at 5 high 5 long.


While I can't specifically answer the question above without the graph or supply and demand equations, but we should be able to answer it by shifting the supply curve up by $2, and re-calculating.  I will demonstrate this below with an example:

Review this old post to find what steps are necessary when calculating consumer and producer surplus. 

With this particular problem we need to know where the supply and demand curves intersect the Y axis, and what equilibrium price and quantity are.  For the base case, we know that demand intersects supply at a price of $5, and a quantity of 5 units.  If the cost of a good increases by $2 for every possible quantity, we know that supply is going to shift up/left.  This means that we will have a new equilibrium price and quantity. 

First let’s calculate the consumer and producer surplus for the original problem.  We know that the height of the consumer surplus triangle is 5 (10-5) and the base is 5.  We use the formula for calculating the area of a triangle to get ½*(5*5) = 12.5



We can go through the same process to get producer surplus which is also 12.5

Now if costs increase by $2, the new intersection of supply on the Y axis will occur at $2 (instead of $0).  The new equilibrium price and quantity will be $6 and 4.  This means that the new consumer surplus will be ½*(4*4) or 8.  The new producer surplus will be the same.  When we compare the consumer and producer surplus between these two levels, we see that both consumer and producer surplus has declined by $4.50.  This means that total surplus for this market has declined by $9 as a result of a $2 increase in cost for each unit produced.




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