Question

There is a single production technology available to firms that might choose to operate in the market for hammers. The cost function associated with this technology is given by c(q)=3+3q^2. For any q>0,but the costs of production are equal to zero if q=0.that is c(0)=0 then find marginal cost and Average cost

Answer 1

The cost function associated with the production technology for the market for hammers is given by c(q) = 3 + 3q^2, where q is the quantity of hammers produced. It is given that the cost of production is zero when no hammers are produced, that is, c(0) = 0.

The marginal cost (MC) is the additional cost of producing one more unit of output. It is calculated as the derivative of the cost function with respect to quantity, that is:

MC = d(c)/d(q) = 6q

Therefore, the marginal cost function for this production technology is MC(q) = 6q.

The average cost (AC) is the cost per unit of output, which is calculated by dividing the total cost by the quantity of output, that is:

AC = c(q)/q

Substituting the given cost function, we get:

AC = (3 + 3q^2)/q

Simplifying this expression, we get:

AC = 3/q + 3q

Therefore, the average cost function for this production technology is AC(q) = 3/q + 3q.

Step-by-step explanation: