Answer to Question #156117 in Microeconomics for arsalan

Question

The demand function equation faced by PTCL for its computers is given by: P = 50,000 – 4Q i. Write the marginal revenue equation ii. At what price and quantity marginal revenue will be zero? iii. At what price and quantity will total revenue be maximized?

Answer 1

i) Let's first find the total revenue:

$$TR=PQ,$$ $$TR=(50000-4Q)Q=50000Q-4Q^2.$$

In order to find the marginal revenue, we need to take the derivative:

$$MR=\dfrac{dTR}{dQ}=\dfrac{d}{dQ}(50000Q-4Q^2)=50000-8Q.$$

ii) Let's first find the quantity at which the marginal revenue would be zero:

$$MR=0,$$ $$50000-8Q=0,$$ $$Q=\dfrac{50000}{8}=6250.$$

Finally, we can find the price at which the marginal revenue would be zero by substituting $Q$ into the demand function:

$$P=50000-4\cdot6250=25000.$$

iii) The marginal revenue equals zero when the total revenue curve has reached its maximum value (in other words, the total revenue is maximized). Thus, the total revenue will be maximized at price 25000 and quantity 6250.

Answer:

i) $MR=50000-8Q.$

ii) $P=25000, Q=6250.$

iii) $P=25000, Q=6250.$