Question

Suppose that Nokia has a monopoly in the market for 5g base stations. In order to construct a network with Q base stations, it costs Nokia TC =8Q+50 and hence the marginal cost is MC=8.

(a) The demand for 5g base stations is Q=12−0.25P. Find the level of output that maximizes Nokia’s profits. What price is Nokia charging? What is the profit?

(b) What level of output would maximize total surplus in the 5g base station market? How much more surplus the market generates compared to the monopolistic market outcome?

(c) If the government provide Nokia a subsidy of S for every unit of 5g base station produced, which will decrease the marginal cost to MC=8-S, what quantity would Nokia choose as a function of S? How much more will Nokia produce when the subsidy S increases by one unit.

(d) Find the choice of subsidy S if the government want to induce Nokia to produce the efficient quantity from part (b), i.e. the output level that maximizes total surplus.

(e) Suppose the government knew the demand and production functions. Find a price regulation the government could impose that would induce Nokia to maximize total surplus, i.e., produce the efficient quantity from part (b).

(f) An alternative price regulation is to impose a price ceiling ?̅ = ???. Discuss why someone might prefer this alternative price regulation over the one from part (e).

Answer 1

TC =8Q+50

MC=8

a)

The demand for 5g base stations is Q=12−0.25P

Calculate inverse demand curve: 0.25P=12-Q

P= 48-4Q

When Q=0, Pm=48

TR= P*Q= 48Q-4Q2

MR= Differentiate TR wrt Q= 48-8Q

To find profit maximizing level of output. The condition is:

MR=MC

48-8Q=8

8Q=40

Q*=5

P*=48-4Q= 28

Profit= TR-TC= P*Q-8Q-50= 28*5-8*5-50= 140-40-50= 50

Total surplus= 1/2(Pm-P*)Q*= 1/2(48-28)5= 1/2(20)5= 50 square units

b)

Level of output that would maximize total surplus, Condition:

P=MC

48-4Q=8

4Q=40

Q**=10

P**=8

Total surplus= 1/2(Pm-P**)Q**=1/2(48-8)(10)= 40*5= 200 square units

So rise in total surplus by 150 square units.

c) MC=8-S

To find profit maximizing level of output. The condition is:

MR=MC

48-8Q=8-S

40+S= 8Q

Q= (40+S)/8

To find out change in Q due to a unit change in S: Differentiate Q with respect to S

dQ/dS= 1/8= 0.125

If S change by 1 unit then Q will change by 0.125 units.

d)

From part b: Q=10

10= (40+S)/8

80=40+S

S=40

To induce producer to produce where total surplus will maximize the government need to provide subsidy of 40.