Question

Based on market research, a film production company in Ectenia obtains the following information about the demand and production costs of its new DVD:

Demand: P=1000-10Q
Total Revenue: TR=1000Q-10Q²
Marginal Revenue: MR=1000-20Q
Marginal Cost: MC=100+10Q
Where Q indicates the number or copies sold and P is the price in Ectenian dollars.

A. Find the price and quantity that maximizes the company’s profit
B. Find the price and quantity that would maximize social welfare
C. Find out Dead weight loss

Answer 1

[REMOVED]

Answer 2

A. Q=30 P=700

B. Q=45 P=550

c. DWL= 2250

Answer 3

for profit maximization : MR = MC

=>1000-20*Q = 100+ 10*Q

=> 900 = 30*Q

=> Q = 30

P = 1000-10* 30 = 700

for social welfare maximization: MC = P

=> 1000-10*Q = 100 + 10*Q

=> 900 = 20*Q

=> Q= 45

=> P = 1000 - 10*45 = 550

DWL = 0.5*(P2-P1)*(Q2-Q1) = 0.5*(700-550)*(30-45) = 0.5*150*-15 = -1125

Answer 4

Given Data:

Denand: \(\mathrm{P}=1000-10 Q\)

Total Revenue: TR-1000Q-10QZ

Marginal Revenue: MR=1000-20Q

Marginal Cost: MC-100-10Q

According to the given data, the firm seems to be operating in a monopoly.

In a market, the maximizing quantity is obtained by equating Marginal

Revenue \((M R)\) with Marginal cost \((MC)\)

Therefore, On equating Marginal Revenue with Marginal cost, we get the maxininding quantity

$$ \begin{aligned} &M R=M C \\ &1000-20 Q=100+10 Q \\ &\Rightarrow 30 Q=900 \\ &\Rightarrow Q=\frac{900}{30} \\ &\Rightarrow Q=30 \text { Units. } \end{aligned} $$

Therefore, the maximising units are 30 Units.

Therefore to obtain the maximiding price, we calculate the price for 30 units by substituting it in the price equation.

$$ P=1000-10 Q $$

On Substitution, we get

$$ \begin{aligned} &\Rightarrow P=1000-10(30) \\ &\Rightarrow P=1000-300 \\ &\Rightarrow P=5700 \end{aligned} $$

Therefore the maximizing price is 5700

The company maximizes its profit at 30 units with price \(\$ 700\)