Consider a competitive firm that can sell its products at a price of p=10 $/unit. It's variable cost function is given by VC(q)=q^2/1000, and it has SFC=FC=$1000.
What is the amount supplied by the firm?
To find the amount supplied by the firm, we need to determine the level of output (quantity) at which the firm is willing to supply its products. This can be found by equating the firm's marginal cost (MC) to the market price (p).
First, let's calculate the marginal cost (MC) function. The marginal cost is the derivative of the variable cost function with respect to output (q).
VC(q) = q^2/1000
To find MC, we differentiate VC with respect to q:
MC(q) = d(VC)/dq
MC(q) = (2q/1000)
Now, let's set MC equal to the market price (p) and solve for q:
(2q/1000) = 10
Multiply both sides by 1000:
2q = 10000
Divide both sides by 2:
q = 5000
So, the amount supplied by the firm is 5000 units.