Answer to Question #301776 in Economics of Enterprise for Leonidos

Question

14. The demand equation faced by Mercantile Communication for its personal computer is given by P = 10,000 – 4Q. a. Write the marginal revenue equation. b. At what price and quantity will marginal revenue be zero? c. At what price and quantity will total revenue be maximized? 4 d. If price is increased from $ 6,000 to $ 7,000, what will be the effect on total revenue? What does this imply about price elasticity?

Answer 1

a. Write the marginal revenue equation.

TR = PQ,

TR=(10000-4Q)Q=10000Q-4Q²

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

$$MR=\dfrac{dTR}{dQ}=\dfrac{d}{dQ}(10000Q-4Q^2)=10000-8Q.$$

Therefore, the marginal revenue equation is 10000-8Q.

b. At what price and quantity will marginal revenue be zero?

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

$$MR=0,$$ $$10000-8Q=0,$$ $$Q=\dfrac{10000}{8}=1250$$

The quantity at which marginal revenue is zero is 1250 computers.

Then, we can calculate the price where the marginal revenue would be zero:

We will substitute $Q$ into the demand function:

$$P=10000-4\cdot1250=5000.$$

Therefore p = $ 5000

c. At what price and quantity will total revenue be maximized?

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 5000 and quantity 1250

d. If the price is increased from $ 6,000 to $ 7,000, what will be the effect on total revenue? What does this imply about price elasticity?

Given Q = $\frac{10000-P}{4}$

The quantity for 6000 is: Q = $\frac{10000-6000}{4}$ = 1000

The quantity for 7000 is: Q = $\frac{10000-7000}{4}$ = 750

Quantity change is 250 computers while price change is $ 1000

E_p = $\frac{ΔP}{ΔQ} = \frac{1000}{750} = 1.33$

Therefore, the price elasticity is 1.33

Because the price elasticity is greater than, we will consider the computer price is elastic. An increase in price results in a decrease in quantity demanded.