Assume that a firm's marginal cost is $10 and the elasticity of demand is -2. We can conclude that the firm's profit maximizing price is approximately:

A) $20.
B) $5.
C) $10.
D) The answer cannot be determined without additional information.

We can use the formula for profit maximization:
Marginal Revenue = Marginal Cost
For a firm with a linear demand curve, we know that:
Elasticity of Demand = (Price / Quantity) x (1 / Slope of Demand Curve)
Since the elasticity of demand is -2 and the slope of the demand curve is negative, the absolute value of the elasticity is equal to the price/quantity ratio. We can set this equal to -2 and solve for the price:
2 = (Price / Quantity) x (1 / Slope of Demand Curve)
2 = (Price / Quantity) x (1 / -1)
Price / Quantity = -2
Price = -2 x Quantity

Now we can substitute this into the equation for total revenue:
Total Revenue = Price x Quantity
Total Revenue = (-2 x Quantity) x Quantity
Total Revenue = -2Q^2

We take the derivative of total revenue to find marginal revenue:
Marginal Revenue = -4Q

Setting marginal revenue equal to marginal cost, we get:
-4Q = 10
Q = -2.5

Since we can't have a negative quantity, we take the absolute value to get a price of:
Price = $20