A monopolist has set her 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:

Question

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The monopolist sets output where marginal revenue equals marginal cost to maximize profits. We are given that marginal revenue is $20. To find the optimal price, we need to know the price elasticity of demand, which is -2.0. We can use the formula:

Price elasticity of demand = (% change in quantity demanded) / (% change in price)

To maximize revenue, the monopolist should increase price if the elasticity is less than 1, keep price constant if the elasticity is equal to 1, and decrease price if the elasticity is greater than 1. Since the elasticity is -2.0, the monopolist should increase price. We can use the formula:

Marginal revenue = Price x (1 + 1 / absolute value of price elasticity of demand)

Solving for price, we get:

$20 = Price x (1 + 1 / 2)

$20 = Price x 1.5

Price = $13.33

Since this is below the profit maximizing price, we know that the optimal price must be higher. We can try $40:

$20 = $40 x (1 + 1 / 2)

$20 = $40 x 1.5

Price = $40

Therefore, the profit maximizing price is approximately $40.

A Monopolist Has Set Her Level of Output to Maximize