Question

Consider a natural monopoly with the following total cost function: TC= 1000 + 20Q and the demand given by P = 140 - 2Q. If you would like to eliminate the deadweight loss completely, what pricing would you suggest that the government imposes on this monopoly.

P=MC=20Q and a subsidy to make sure that the monopoly can cover the fixed cost

P=AC=20 and a tax to move the quantity traded to the efficient level

None of the other answers is correct

P=80 and no subsidy since the monopolist profit is maximized

P=MC=20 and a subsidy to make sure that the monopoly can cover the fixed cost

Answer 1

TC= 1000 + 20Q

AC= TC/Q= 1000/Q +20

MC= Differentiation of TC with respect to Q= 20

Variable cost(VC)= 20Q

Average variable cost(AVC)= VC/Q= 20Q/Q= 20

MC=AVC

Fixed cost(FC)= 1000

P = 140 - 2Q

In natural mnopoly, AC and MC is always downward sloping and AC>MC.

If MR=MC Condition is use which cause deadweight loss, So P=MC condition will be used.

P=MC

140-2Q=20

120= 2Q

Q= 60 Quantity at which there will be no deadweight loss

P=20 Price at which there will be no deadweight loss

Here P=AVC so this price can cover variable cost but P<AC which implies monopolist faces losses due to fixed cost.

So government should subsidized so that it can cover its fixed cost.

P=MC=20 and a subsidy to make sure that the monopoly can cover the fixed cost