The price elasticity of demand for melocotones is constant and equal to -2.The melocotone market is controlled by two Cournot duopolists who have different cost functions.One of the duopolists has a constant marginal cost of $675 per ton and produces 50% of the total number of melocotones sold.The equilibrium price of a ton of melocotones must be
A)$1,800.
B)$450.
C)$900.
D)$675.
E)$1,350.

Question

Quizplus · Accepted Answer

We can use the formula to calculate the equilibrium quantity for each duopolist:
q1 = (1/3)*(P - MC)/PES
q2 = (2/3)*(P - MC)/PES

where q1 and q2 are the quantities produced by each duopolist, P is the price, MC is the marginal cost, and PES is the price elasticity of demand.

Since one duopolist produces 50% of the total number of melocotones sold, we know that q1 + q2 = Q/2, where Q is the total quantity sold in the market.

Setting q1 + q2 = Q/2 and solving for P, we get:

P = (MC + PES*Q/3)/(1 + 2*PES/3)

Plugging in the given values, we get:

P = (675 + (F1F1F1S1 - F1F1F102)*Q/3)/(1 + 2*(F1F1F1S1 - F1F1F102)/3)

We do not have a specific value for F1F1F1S1 - F1F1F102, so we cannot calculate a numerical answer. However, we can make some general observations about how the equilibrium price will change based on the value of F1F1F1S1 - F1F1F102:

- If F1F1F1S1 - F1F1F102 is positive (i.e. demand is elastic), then P will be greater than MC. This makes sense, since the duopolists can charge a higher price when demand is more responsive to changes in price.
- If F1F1F1S1 - F1F1F102 is zero (i.e. demand is unit elastic), then P will be equal to MC. This also makes sense, since the duopolists cannot charge a premium for their product if demand is only willing to pay the cost of production.
- If F1F1F1S1 - F1F1F102 is negative (i.e. demand is inelastic), then P will be less than MC. This is somewhat counterintuitive, but it reflects the fact that the duopolists have market power and are able to charge a higher price than marginal cost even when demand is not very responsive.

Based on these observations, we can eliminate answer choices A, B, and D, since they imply that the equilibrium price is either equal to or less than the marginal cost of production. The remaining answer choice, C, is consistent with the possibility that demand is elastic or unit elastic, and is therefore the best answer. We cannot determine a specific numerical value for the equilibrium price, however.

The Price Elasticity of Demand for Melocotones Is Constant and Equal