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Homework answers / question archive / The market demand for a good is P = 70 - 1

The market demand for a good is P = 70 - 1

Economics

The market demand for a good is P = 70 - 1.5Q. The good can be produced at a constant cost of $10. How much deadweight loss is created if the market is served by a monopolist as opposed to a competitive market?

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Given data,

The market demand for a good is P = 70 - 1.5Q.

The good can be produced at a constant cost of $10.

P = 70 - 1.5Q, MC =10$

Competitive market; P=MC

70 - 1.5Q = 10

1.5Q = 60

Q= 40 And P=10

In a monopoly MR = MC

TR = P * Q

(70 - 1.5Q)* Q = 70Q- 1.5Q2

Then we derivate TR with respect to Q

MR= dTR/dQ = 70- 3Q

So,

70-3Q= 10

3Q= 60

Q=20

Put Q=20 in P=70 - 1.5Q

then P=40

Formula to Calculate Deadweight Loss = (1/2)* (P2 - P1) * (Q1 - Q2).

Here P2= 40 and P1= 10 and Q1=40 and Q2=20

Dead weight loss = (1/2) *(40-10) * (40-20)

= 300Ans