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.

Answer 1

(a) demand for 5g base stations = Q=12−0.25P

From this, find out the value of P

....... (1)

Now, total revenue (TR) can be calculated by multiplying price and quantity

Marginal revenue is obtained by differentiating TR with respect to quantity

Profit-maximization condition for a monopolist involves equating MR and MC

Hence, Nokia produces 5 units of 5g base stations.

Put Q=5 in (1)

Therefore, price Nokia is charging = $28

Profit can be calculated by subtracting total cost from total revenue

Therefore, the Nokia earns $50 as profits when it sells 5 units at a price of $28

(b) If maximization of total surplus is the purpose, then Nokia should produce at a perfectly competitive level. This happens when P=MC

Hence, Nokia should produce 10 units in order to maximize the total surplus.

Put Q = 10 in (1)

Therefore, Nokia charges $8 (which is also equal to marginal cost)

Figure 1

Now, the area highlighted in red indicates the dead weight loss or the loss of welfare if Nokia decides to act as a monopoly as compared to a perfectly competitive firm

Therefore, market would produce $50 more surplus compared to the monopolistic market outcome.

(c) When a subsidy of S is provided and MC become = 8 -S. Then quantity produced by Nokia can be found out by equating new Marginal cost to marginal revenue

Therefore, after imposition of S subsidy, Nokia would produce (5 - S/8) amount of quantity.

If the subsidy increase by 1 unit, new marginal cost becomes = 7-S.

When subsidy is raised by 1 unit, the quantity increases by 10 units

(d) Government should shift the MC curve of Nokia such that the new MC curve intersects (old) MR at q = 10 (perfectly competitive price). When Q=10, MR = 48-8 *10 = -32

When this happens, Nokia would produce 10 units of base station (which are the units produced in perfectly competitive market)

MC = 8-S

Put MR = MC

-32 = 8-S

S=40

Hence, a subsidy of $40 is to given by the government so as to make the monopolist produce the output level that maximizes total surplus.