Answer to Question #283526 in Microeconomics for Alina shaikh

Question

Question

A firm has the following information on production and costs from past data:

Output (Y) 0 6 12 18

Total Cost (TC) 9 2775 5361 8199

If the total cost function is known to be TC=aY3+bY2+kY+f, and the demand for the product of the firm is Y=320-(1/2)P. answer the following:

Determine the coefficient of the cubic cost function.

Derive all cost and revenue curves and the profit function.

Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all points.

Answer 1

The coefficient of the cubic cost function is a.

TC = FC + VC, all theses cost curves are upward-sloping.

Total revenue function is $TR = P×Y = 640Y - 2Y^2.$

The profit function is TP = TR - TC.

The MC cuts the AVC when AVC is at its minimum point. MC is the cost of producing the next unit. If cost of producing next unit is less than the average, then it means that marginal cost is pulling down average variable cost.