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:

Question

Quizplus · Accepted Answer

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

Assume That a Firm's Marginal Cost Is $10 and the Elasticity