When we are given an expression for the Short Run Total Cost Curve (for eg: 8 +

Question

3Q - 1.5Q^2 + 0.25Q^3), how do you derive expressions for the following:

1. Average Fixed Costs
2. Average Viarable Costs Curve
3. Marginal Costs Curve
4. Short Run Supply Curve

I also have a second question:
In perfect competition, if you are given the firm's total cost curve (for eg:
450 + 15Q + 2Q^2), and you are also given the Price, how do you find out the
firm's profit maximising level of output and it's profit/loss level?

An answer to either of these questions or preferably both would be great.
Thank you.

Your equation: TC = 8 + 3Q - 1.5Q^2 + 0.25Q^3
1) Total fixed costs are 8. So avg fixed costs are 8/Q.
2) Ergo Avg variable costs are (TC-8)/Q
3) Marginal cost is the first derivitive of total costs. (use calculus)
4) Short run supply is marginal cost curve.

Always, always, maximize when MC=MR
For a perfect competitor, MR=Price.
MC is the first derivitive of TC.
Profit/loss = Total revenue - Total cost. and TR=P*Q. Just plug in your maximizing Q.

Answer 1

mc=d/dq(8+3Q - 1.5Q^2 + 0.25Q^3)
=3+2*1.5q+3*0.25q2