The market demand for gadgets is given by Q d =100- 3 p , where Q d is the quant

Question

The market demand for gadgets is given by Qd=100-3p , where Qd is the quantity of gadgets demanded and p is the price of a gadget in dollars. The market supply is given byQs= p , where Qs is the quantity of gadgets supplied. The production of gadgets releases a toxic effluent into the water supply. The marginal external cost can be described by MEC(Q)= 2Q .

a) Compute consumer surplus, producer surplus and the cost pf pollution in the market equilibrium.

b) Compute consumer surplus, producer surplus and the cost pf pollution in the social optimum.

c) Suppose the government is considering imposing a tax of $T per unit on the producers. Find the level of the tax that ensures the socially optimal amount of gadgets will be produced in a competitive equilibrium.

Explanation / Answer

Consumer surplus is an economic measure of consumer satisfaction, which is calculated by analyzing the difference between what consumers are willing to pay for a good or service relative to its market price. A consumer surplus occurs when the consumer is willing to pay more for a given product than the current market price.

Producer surplus is an economic measure of the difference between the amount that a producer of a good receives and the minimum amount that he or she would be willing to accept for the good. The difference, orsurplus amount, is the benefit that the producer receives for selling the good in the market.

At euilibrium,

Qd=Qs

100-3p=p

4p=100

p=25. q=25.

Then we can say the producer surplus is=1/2(25*25)=312.5

Qd=100-3p

when q=0,then

3p=100

p=100/3=33.33

then consumer surplus=1/2*33.33*25=416.62

here cost is=(25*25)=625.

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