A monopolist has set the level of output to maximize profit. The firm's marginal revenue is $20 and the price elasticity of demand is - 2.0. The firm's profit maximizing price is approximately:
A)$10.
B)$20.
C)$40.
D)$0.

Question

Quizplus · Accepted Answer

The profit-maximizing price for a monopolist is where marginal revenue (MR) equals marginal cost (MC), or MR=MC. However, we are given that MR=$20. 
To find MC or price elasticity of demand (PED), we can use the formula: PED = (% change in quantity demanded) / (% change in price). Since PED is negative (as the price increases, quantity demanded decreases), we use the absolute value of PED. In this case, we are given that PED = -2.0, so |PED| = 2.0. 
We can set up the following equation: |PED| = (new quantity - old quantity) / (new price - old price) * (old price / old quantity).
Solving for the new price, we get: 
2.0 = (1 - old quantity / new quantity) / (new price / old price)
2.0 * (new price / old price) = 1 - old quantity / new quantity
2.0 * (new price / old price) + old quantity / new quantity = 1
We know that at the profit-maximizing output level, PED = 1 (unit elasticity), so we can substitute that value in for |PED| and solve for the new price: 
1 = (1 - old quantity / new quantity) / (new price / old price)
new price / old price = (1 - old quantity / new quantity)
new price = old price * (1 - old quantity / new quantity)
Since we are assuming the monopolist is currently at the profit-maximizing output level, we can plug in the given values: 
new price = $20 * (1 - old quantity / old quantity) = $20 
Therefore, the profit-maximizing price is $20, which is closest to Choice C.

A Monopolist Has Set the Level of Output to Maximize