Question

Suppose total cost is ??(?) = ?3 − 6?2 + 12? + 2.

a. What are the formulas for marginal cost, average cost, average variable cost, and fixed

cost? Graph each of these carefully.

b. At what quantity does marginal cost equal average cost? Prove that average cost

reaches its minimum point at this quantity, and that this is true generally, not just for

this total cost function.

c. Suppose that the price of output is ? = 25. What is the profit maximizing choice of

quantity for this producer?

d. How much would this producer produce if price were 10, 15, 20, or 30? Graph these

points with quantity on the x axis and price on the y axis.

Answer 1

a. What are the formulas for marginal cost, average cost, average variable cost, and fixed cost? Graph each of these carefully.

Marginal Cost = Change in Total Cost / Change in Quantity

Or, Marginal Cost =

Average Cost = Total Cost / Quantity

Average variable cost = Variable Cost / Quantity

Fixed cost = Total Cost - Variable Cost

b. At what quantity does marginal cost equal average cost? Prove that average cost reaches its minimum point at this quantity, and that this is true generally, not just for this total cost function.

Marginal cost equals average cost at the 3rd quantity, We can see from the table that marginal cost at its minimum at the 3rd quantity.

In a similar manner, marginal cost curve intersects the other cost curves when they are at their minimum. This can be seen from the graph.

c. Suppose that the price of output is ? = 25. What is the profit maximizing choice of quantity for this producer?

Profit is maximum at 5th unit where MR = MC

Total Revenue = Quantity * Price

Profit = Total Revenue - Total Cost

d. How much would this producer produce if price were 10, 15, 20, or 30? Graph these points with quantity on the x axis and price on the y axis.

Maximum profit is otained where MR = MC, using this principle the producer will produce the following quantities