# Finding Optimal Output Level etc.

Redstone Clayworks, Inc. is located in Sedona, Arizona and manufactures clay fire pits for patios. They are one of about two dozen firms around the world that manufacture and sell clay fire pits for retailers such as Home Depot Lowe's Front Gate, and other upscale home product chains. There is virtually no product differentiation; a clay fire pits is a clay fire pit.

The spreadsheet below gives some of Redstone's production cost data. Enter this data in your own Excel spreadsheet. Add columns 5, 6, 7, and 8 to show respectively average fixed cost (AFC), average variable cost (AVC), average total cost (ATC), and short-run marginal cost (SMC).

Q TC TFC TVC

0 5000 5000 0

100 10000 5000 5000

200 19000 5000 14000

300 27000 5000 22000

400 38000 5000 33000

500 50000 5000 45000

600 66000 5000 61000

700 84000 5000 79000

800 104000 5000 99000

900 126000 5000 121000

1000 150000 5000 145000

The world market demand and supply curves for clay fire pots intersect at $190 per unit. Add columns 9, and 10 to show, respectively total revenue (TR) and marginal revue (MR). Add column 11 to show profit (i.e., TR-TC). Add column 12 to show profit per unit (i.e., average profit). Add column 13 to show profit margin (i.e, price minus average total cost).

1. If Redstone wanted to minimize average total cost, it would produce how many units?

2. If Redstone wishes to maximize profit MARGIN, it should produce how many units.

3. What level of output should the manager of Redstone choose to produce? Explain briefly.

4. Now triple the fixed costs to 15,000 in your spreadsheet. How does this change your answer to question 4. Explain briefly.

5. Suppose that Nancy Pelosi declares that clay fire pits are causing global warming, and demand for fire pits shrinks substantially in the U.S. (especially in California). Fire pit prices fall worldwide to $65. Now, the manager of Redstone should produce how many units? Explain your answer.

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#### Solution Preview

Please refer to attached file for missing tables.

1. If Redstone wanted to minimize average total cost, it would produce how many units?

Refer to above table, ATC is minimized at Q=300 units. It should produce 300 units.

2. If Redstone wishes to maximize profit MARGIN, it should produce how many units.

Refer to above table, Profit margin is maximized at Q=300 units. It should produce 300 units.

3. What level of output should the manager of Redstone ...

#### Solution Summary

Solution describes the steps to find out output levels for minimum average total cost, maximum profit margin and optimal profit. Tables attached in Excel.

Marginal Analysis Global Corp

(see attached for full problem description)

1

Global Corp. sells its output at the market price of $9 per unit. Each plant has the costs shown below:

What is the profit at each plant when operating at its optimal output level?

2

Suppose that you can sell as much of a product (in integer units) as you like at $61 per unit. Your marginal cost (MC) for producing the qth unit is given by:

MC=9q

This means that each unit costs more to produce than the previous one (e.g., the first unit costs 9*1, the second unit (by itself) costs 9*2, etc.).

If fixed costs are $50, what is the optimal output level?

Please specify your answer as an integer.

3

Assume that a competitive firm has the total cost function:

TC = 1q3 - 40q2 + 710q + 1700

Suppose the price of the firm's output (sold in integer units) is $550 per unit.

Using tables (but not calculus) to find a solution, what is the total profit at the optimal output level?

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