Question

Suppose a honey farm is located next to an apple orchard and each acts as a competitive firm. Let the amount of apples produced be measured by A, and the amount of honey produced be measured by H. The two firms’ cost functions are cH (H) = H2 /100 and cA(A) = (A2 /100) ‑ H. The price of honey is $2 and the price of apples is $3.

(a) If the firms each operate independently, the equilibrium amount of honey produced will be _________and the equilibrium amount of apples produced will be __________

Answer 1

The equilibrium amount of honey produced will be 100, and the equilibrium amount of apples produced will be 300.

Step-by-step explanation:

In a perfectly competitive market, a firm maximizes its profit by producing a quantity where the price is equal to the marginal cost. To find the equilibrium amount of honey and apples produced, we need to set the price of honey equal to the marginal cost of production (§H) and the price of apples equal to the marginal cost of production (§A).

Given that the price of honey is $2 and the price of apples is $3, we have the following:

$2 = §H = §H^2/100

Solving for §H, we have:

§H = 100

Similarly, for apples, we have:

$3 = §A = (§A^2/100) - §H

Solving for §A, we have:

§A = 200 + §H

Therefore, the equilibrium amount of honey produced (§H) is 100, and the equilibrium amount of apples produced (§A) is 300.