Question

Given information, cost equation C(Q), Marginal cost MC(Q), and its demand for elasticity equation

Q(p). ?(?) = 0.5?3 − 20?2 + 282.5?

MC(?) = 1.5?2– 40? + 282.50

?d(?) = 16 − (1/20)?

The government decides that the lack of competition in this market is detrimental to the economy and, for that reason, government intervention is required. The governor proposes regulating the price of electricity or nationalizing the power plant. Do you think the governor is right? [Hint: Is there a deadweight loss (DWL) in this monopoly that justifies an intervention?]

Answer 1

First, we have to check the current equilibrium quantity and price and MC.

now demand equation is given as, Q=16-(1/20)P

or, we can write P=320-20Q or AR(average revenue)=320-20Q

now total revenue=ARXQ=320Q-20Q^2

now MR= d/dQ(TR)=320-40Q

now profit maximising condition for the electricity-producing company will be, MC=MR

or 1.5Q^2-40Q+282.5=320-40Q

or, 1.5Q^2=320-282.5=37.5

or Q^2=25

hence Q=5 (because Q cannot be negative)

now at Q=5, P=AR=320-20x5=220

And MC=120

and AC=195

we know a competitive social welfare maximising equilibrium is set at P=MC

hence social welfare maximising output will set in,

1.5Q^2-40Q+282.5=320-20Q

or, Q(sw)=15 and here price P(sw) will be, 20

but now the equilibrium output is set at P>MC

that means there are some excess capacity left (producing 5 instead of 15) utilising which we can increase the total welfare of people and cut down price(220 instead of 20). hence there is a deadweight loss in this scenario. In the diagram,

deadweight loss is represented by the red shaded area.

Hence governors decision is right.

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