Based on market research, a film production company in Ectenia obtains the following information about the demand and production costs of its new 4K Blu-ray: Demand: P=1000-10Q Total revenue: TR=1000Q-10Q^2 Marginal revenue: MR=1000-20Q Marginal cost: MC=100+10Q where Q indicates the number of copies sold and P is the price in Ectenian dollars. a) Find the price and quantity that maximise the company's profit. b) Find the price and quantity that would maximise social welfare. c) Calculate the deadweight loss from monopoly. d) Suppose, in addition to the costs above, the director of the film has to be paid.The company is considering four options: i, a flat fee of 2000 Ectenian dollars. ii, 50 per cent of the profits. iii, 150 Ectenian dollars per unit sold. iv 50 per cent of the revenue. For each option, calculate the profit-maximising price and quantity. Which, if any, of these compensation schemes would alter the deadweight loss from monopoly? Explain.

a) To maximize profit, the company should set Marginal Revenue (MR) equal to Marginal Cost (MC). So, we have:

1000 - 20Q = 100 + 10Q 900 = 30Q Q = 30

Substitute Q = 30 into the demand equation to find the price:

P = 1000 - 10*30 = 700

So, the price and quantity that maximize the company's profit are P = 700 and Q = 30.

b) To maximize social welfare, the company should set Price (P) equal to Marginal Cost (MC). So, we have:

P = 100 + 10Q 1000 - 10Q = 100 + 10Q 900 = 20Q Q = 45

Substitute Q = 45 into the demand equation to find the price:

P = 1000 - 10*45 = 550

So, the price and quantity that maximize social welfare are P = 550 and Q = 45.

c) The deadweight loss from monopoly is the difference between the quantity that maximizes social welfare and the quantity that maximizes profit, times the difference in price, divided by 2. So, we have:

Deadweight loss = 0.5 * (45 - 30) * (700 - 550) = 0.5 * 15 * 150 = 1125

d)

i) The flat fee does not affect the marginal cost, so the profit-maximizing price and quantity are the same as in part a), P = 700 and Q = 30.

ii) If the director gets 50% of the profits, the company's marginal cost doubles, so we have:

1000 - 20Q = 200 + 20Q 800 = 40Q Q = 20

Substitute Q = 20 into the demand equation to find the price:

P = 1000 - 10*20 = 800

So, the profit-maximizing price and quantity are P = 800 and Q = 20.

iii) If the director gets 150 per unit sold, the company's marginal cost increases by 150, so we have:

1000 - 20Q = 250 + 10Q 750 = 30Q Q = 25

Substitute Q = 25 into the demand equation to find the price:

P = 1000 - 10*25 = 750

So, the profit-maximizing price and quantity are P = 750 and Q = 25.

iv) If the director gets 50% of the revenue, the company's marginal cost doubles, so we have:

1000 - 20Q = 200 + 20Q 800 = 40Q Q = 20

Substitute Q = 20 into the demand equation to find the price:

P = 1000 - 10*20 = 800

So, the profit-maximizing price and quantity are P = 800 and Q = 20.

The compensation schemes that would alter the deadweight loss from monopoly are ii), iii), and iv), because they change the company's marginal cost and therefore the profit-maximizing quantity.