Calculating changes in consumer and producer surplus after regulating a monopoly

This economics question and answer goes over how to calculate changes in consumer and producer surplus with limited information.  The question asks about a monopoly market that is subject to government regulation in an attempt to increase societal welfare (or total economic surplus).  The actual question being looked at is:

A refrigerator monopolist, because of strong economies of scale, could charge a price of $120 and sell 45 refrigerators in Iceland and its average cost would be $60. On the other hand, the Iceland Planning Commission has determined that 5 refrigerator suppliers would be sufficiently competitive to make price equal to average cost. The five-firm equilibrium would yield a price of $100 and a total output of 50 refrigerators.

a. Consumer surplus under the five-firm industry organization would be larger than under monopoly. If the demand curve is linear, by how much is consumer surplus higher

b. Producer surplus under monopoly is larger - by how much?

To answer the question, we need to find what the area of the rectangle and triangle is between these two different demand points.  We can see from the graph that we need to find the areas of B and C because these areas represent the change in consumer surplus. --Note that each of these points were given from the information above, and that a straight line connecting them is assumed-- The area of B is calculated by multiplying the base (45) times the height (20) to get $900, and the area of C is calculated using the area of a triangle method by multiplying ½ of the base (5) times the height ($20) to get $50.  When we add the area of B and C together, we get a total change in consumer surplus of $950.

To get the producer surplus, we do the same sort of analysis but in reverse.  We know Producer surplus before the regulation is equal to the areas of A, B and C.  --Note that each of these points were given from the information above, and that a straight line connecting them is assumed-- After the monopoly regulation, the producer surplus goes down by the area of C (because of lower prices) but goes up by the area of D because of larger sales.  The area of C is equal to $900 (45*20) which is directly transferred to consumer surplus.  The area of D is equal to ½ of the height of the triangle 40 (100-60) times the base of the triangle 5 (50-45).  This ends up being $100.  So the net change in producer surplus is $100-$900 or -$800.

A natural third question would be to ask how much national or total surplus has changed based on the monopoly regulation by the government.  Since consumer surplus went up by $950, and producer surplus declined by $800, the net gain to society is $150 so both economists and society would prefer this regulation because it has resulted in a higher total surplus than letter the monopoly operate unregulated.

Keep in mind that this answer has assumed that the lines are linear between the two points mentioned, and that we don’t necessarily need to know where the intercepts are (or even the slopes for the matter) to calculate the CHANGE in consumer and producer surplus.

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