if there are no fixed costs and marginal cost is constant at $56, the price elasticity of demand at the profit-maximizing level of output is closest to
A)-0.28.
B)-7.09.
C)-3.55.
D)-14.18.
E)-0.14.

Question

Quizplus · Accepted Answer

In a situation with no fixed costs, profit maximization occurs at the point where marginal revenue equals marginal cost. Since there are no fixed costs and assuming perfect competition, the price equals the marginal revenue. Therefore, at the profit maximizing output level, price equals marginal cost ($56).

Price elasticity of demand can be calculated using the formula:

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

Assuming a linear demand curve, the percentage change in quantity demanded will be equal to the percentage change in price. Therefore, we can simplify the formula as follows:

Price elasticity of demand = 1 / (slope of demand curve x price/quantity)

Since marginal cost is constant and equal to $56, we can assume that this is also the equilibrium price. Therefore, we only need to know the slope of the demand curve at the profit-maximizing quantity.

If the slope of the demand curve is -0.5 (i.e. if price elasticity of demand is 0.5), then the price elasticity of demand at the profit-maximizing level of output would be:

Price elasticity of demand = 1 / (-0.5 x 56/100) = 1 / (-0.28) = -3.55

Therefore, the absolute value of price elasticity of demand would be 3.55, which is closest to choice C (3.55).

If There Are No Fixed Costs and Marginal Cost Is