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Homework answers / question archive / There are forty consumers in an economy who purchase a drug to relieve the pain of arthritis
There are forty consumers in an economy who purchase a drug to relieve the pain of arthritis. They think that the only effective drug is Namebrand. However, the same drug can be bought by its chemical name acethistestamine, or ace for short. The drug costs $2 to produce no matter what it is called; any quantity demanded can be supplied at that price. The company producing Namebrand exploits consumer ignorance by charging $6 for each unit; that is, the consumers buy Namebrand at $6 per unit, not realizing that ace is a perfect substitute available for only $2. The aggregate demand curve of the 40 uninformed consumers is Q = 400 - 40P. a What would be the value to consumers of knowing that ace and Namebrand are iden- tical? (Answer: $960.) b How much is the deadweight loss due to the consumers' lack of perfect information? (Answer: $320.)
) a) The value to consumers would be the difference between the consumer surplus in both the cases ie when the price is at $6 and when it is at $2.
The graph below shows the area of value added to consumers in case of fall in price, which is the area of trapezium ie ABCD.
Area of trapezium ABCD= 1/2( sum of parallel sides)* area between them.
AB would be the length of one side which is also equal to the quantity purchased when price is 6.
Hence putting the value of P=$ 6 in the aggregate demand equation, we get
Q= 400-40(6)= 400-240=160
Similarly DC is the other parallel side and also the quantity when price is $2. Hence putting it we get
Q=400-40(2)=400-80=320
The distance between parallel sides would be difference in prices is 6-2=$4
Putting to find the area we get
Area of ABCD= 1/2(320+160)*4
=480*2
= 960
Hence the value gained would be $960.
b) The deadweight loss would be the area of triangle BCE in the graph. This is the area which would have been captured when price would have been $2 and hence is a loss to the society.
Area of BCE=1/2*b*h=1/2*(6-2)*(320-160)
=1/2*4*160
=320
Hence the deadweight loss is $320.
(You can comment for doubts)
please see the attached file for the complet solution.
