Question

The inverse demand for organic dog food is given by P₁ = 26 2Q₁ , and the inverse demand for conventional dog food is given by P₂ = 10−Q₂

, where P is the price of dog food in USD//b, and Q is the quantity of dog food in thousand pounds. The cost of producing dog food is C(Q)=2Q. The profit-maximizing quantity of conventional dog food is equal to (1000s):
(a).3
(b).4
(c).2
(d).3

Answer 1

To find the profit-maximizing quantity of conventional dog food, set the marginal cost (MC) equal to the marginal revenue (MR) and solve for Q. The profit-maximizing quantity is 3.

Step-by-step explanation:

To find the profit-maximizing quantity of conventional dog food, we need to compare the marginal cost (MC) and marginal revenue (MR). The MC is the derivative of the cost function, C(Q), which is 2. The MR is the derivative of the inverse demand function, P₂ = 10−Q₂, which is -1. To maximize profit, we need to set MC equal to MR and solve for Q. So, 2 = -1 and Q = 3. Therefore, the profit-maximizing quantity of conventional dog food is 3.