A,B,C refer to the following question

A monopolist is producing iron ore. The quantity Q is measured in tonnes of iron ore per day and can take only non-negative values. Given the current technology, the maximum level of production is Q=180. Suppose that the demand curve facing this monopolist is

Q=200-1/2×P

where P denotes the price of iron ore measured in dollars per tonne, and the total cost of producing iron ore is described by the function:

TC=0.2×Q^2+4×Q+400

The variable TC is measure in dollars per day.

a.

To maximize profits the monopolist will charge a price of

220 $/tonne

210 $/tonne

200 $/tonne

190 $/tonne

180 $/tonne

b.

The marginal cost curve cuts the marginal revenue curve when the output level is

50 tonnes/day

60 tonnes/day

70 tonnes/day

80 tonnes/day

90 tonnes/day

c.

Suppose that the monopolist takes advantage of the corona virus crisis and makes the government incur all the variable costs of producing iron ore, that is, the total cost function now is TC=400 but the monopolist gets all the money for selling iron ore. How much money the monopolist would be making when total profit is maximized?

20,000 $/day

19,600 $/day

17,420 $/day

17,400 $/day

17,300 $/day

## EXPERT ANSWER

a. 220 $/tonne

(Q=200-1/2×P = 200-0.5P

So, 0.5P = 200 – Q

So, P = (200/0.5) – (Q/0.5)

So, P = 400 – 2Q

TR = P*Q = (400 – 2Q)Q = 400Q – 2Q^{2}

MR = d(TR)/dQ = 400 – 2(2Q) = 400 – 4Q

MC = d(TC)/dQ = 2(0.2Q) + 4 = 0.4Q + 4

Monopolist maximizes profit where MR = MC. So,

400 – 4Q = 0.4Q + 4

So, 4Q + 0.4Q = 4.4Q = 400 – 4 = 396

So, Q = 396/4.4 = 90

P = 400 – 2Q = 400 – 2(90) = 400 – 180 = 220)

b. 90 tonnes/day

c. 19,600 $/day

(Profit is maximized when MR = 0

So, 400 – 4Q = 0

So, 4Q = 400

So, Q = 400/4 = 100

P = 400 – 2Q = 400 – 2(100) = 400 – 200 = 200

TR = P*Q = 200*100 = 20,000

Profit = TR – TC = 20,000 – 400 = 19,600)