Based on market research, a film production company in Ectenia obtains the follo

Question

Based on market research, a film production company in Ectenia obtains the following information about the demand and production costs of its n DVD: P-1.200-100 Demand: Total Revenue: TR= 1.200-10Q2 Marginal Revenue: MR 1,200 20Q Marginal Cost: MC=300+ 10Q where Q indicates the number of copies sold and P is the price in Ectenian dollars. Complete the following table by finding the price and quantity that maximize the company's profit and the price and quantity that maximize social Price Quantity (Dollars) (DVDs Scenario Maximizes the company's profit Maximizes social welfare The deadweight loss from the monopoly is $

Explanation / Answer

Profit maximisation condition is ,where MR= MC.

MR = MC

1200 - 20Q = 300 + 10Q

1200-300 = 30 Q

Q= 30 DVDS (profit maximisation quantity)

Put Q=30 in demand function , P= 1200- 10 (30)

P =$ 900 (profit maximisation price)

Social welfare is maximisaed where P = MC

Now , 1200- 10 Q = 300+ 10Q

1200 - 300 = 20 Q

Q = 45 DVDS (Social welfare maximsation quantity)

Put Q= 45 in demand function :

P= 1200- 10 (45)

P =$ 750 (social welfare maximisation price)

Dead weight loss is the area of the triangle = 1/2 (base) (height)

when MR= MC then MC= 300 + 10(30) = $600 and profit maximisation price is $900

Therefore, deadweight loss = 0.5 ( 45-30) (900-600) = 0.5(15) (300) == $2250.

Suppose in addition to the costs, the director of the film has to be paid. Comapny is considering four options: Profit maximisation price and quantity would be affected or not:

1. Flat fee of 2,500 Ectenian dollars

A flat fee of $2500 Ectenian dollars would not alter the profit maximising price and quantity . The deadweight loss would also be unaffected. Price and Quantity is $900 and 30 DVDS respectively . Deadweight loss is $2250.

2. A fee of 50% of the profits

A fee of 50% of profits would also not alter the profit maximising output and price. The deadweight loss would also be unaffected. Same as (1) part .

3. 150 Ectenian dollars per unit sold

The marginal cost of production would rise by 150 Ectenian dollars if the director was paid that amount for every unit sold. Therefore, the new marginal cost would be 300 + 10Q + 150 . MR is the same as in question .

Profit maximising output , is where MR=MC

1200 -20Q = 300 + 10Q + 150

750 = 30Q

Q=25 DVDS

Put Q=25 in deamnd function

P = 1200 - 10(25) = $950

And new MC = 300 + 10(25) +150

MC= $700

With the new MC , Quantity at which social welfare is maximised would change. When P = New MC

Then, 1200-10Q = 700

Q= 50 and P= 700 {under social welfare maximised }

As a result deadweight loss , = (0.5) (50-25) (950 - 700)

= (0.5)(25)(250) = $3125.

4. 50% of the revenue

If the director is paid 50% of the revenue , then total revenue is (1200Q - 10Q2) / 2 = 600Q - 5Q2

MR is = 600- 10Q

So, profit maximising output is where MR=MC

600-10Q = 300+ 10Q

300 = 20 Q

Q = 15 {profit maximising output}

Put Q in demand function

P = 1200 - 10(15)

=1200 -150 = $1050 { profiy maximising price}

Now , MC= 300 + 10(15) = 300 + 150 = $450

Under social welfare maximisation :

P = MC

1200 - 10Q = 450

1200 - 450 = 10Q

750 = 10Q

Q=75 and P = $450 {under social welfare maximising condition}

Now, deadweight loss = (0.5) (75-15) (1050-450)

= (0.5)( 60) (600)

= $18,000.

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