Blog #3

(Part one)

For this experiment, either…

a.     Interview a manager/CEO/owner of a local company or start up (about one product…if they produce multiple products, only focus on one product of good)

Or

b.     Do online research of a local company or local start up (of one product…if they produce multiple products, only focus on one product of good)

Or

c.     Make up/invent your own (hypothetical ) company or start up for one product

Hypothetical Company: Peter Manufacturing Limited

Product Manufactured: Bearings

(Part two)

The company Peter Manufacturing Limited (or Peter) is engaged in the manufacturing of bearings for industrial applications. These bearings are used in a variety of rotating equipment and help to reduce friction between the rotating shaft and casing. Typical applications include pulp and paper mills, power generation companies and other large industrial units.

The company started operations 10 years ago in California and sells across the United States and also exports some bearings to Europe.

After choosing either a, b, or c, write up a synopsis about the company (i.e. what they sell/produce, target demographics, history of the company, etc.)

Then, determine the following:

·       Find total fixed costs--Start up costs (if you can, try to get/make a list of start up costs and dollar amounts. For instance, heating a building, rent, supplies, internet, etc.)

Fixed Costs for a monthly production run of bearings = Rent ($10,000) + Overheads ($10,000) + Utilities ($5000) =

a = $25,000

·       Find variable costs—cost for producing one additional unit/quantity of good

Variable Costs per bearing = Labor ($100) + Material ($150) =

b = $250

·       Determine the price for which the company sells a unit/quantity of good (this will be needed to determine the revenue function. If the company sells one unit for $250, then the revenue function will be R(q) = 250q)

Price per bearing =

p = $1,250

·       Find the cost function

Cost Function =

C(q) = a + bq = 25,000 + 250q

·       Find the revenue function

Revenue Function =

R(q) = pq = 1,250q

·       Find the profit function

Profit Function =

P(q) = R(q) – C(q) = 1,250q – (25,000 + 250q) = 1,000q – 25,000

·       Determine the break-even point value

At break-even point, revenue equals cost, which can be written as follows:

R(q) = C(q)

Hence, 1,250q = 25,000 + 250q

ð  q = 25

ð  R(q) = 1,250q = 1,250 X 25 = $31,250

and C(q) = 25,000 + 250q = 25,000 + 250 X 25 = $31,250

·       Graph the cost function and the revenue function on the same grid and mark the break-even point and its value on the graph

·       Interpret the meaning of the break-even point on the graph and interpret the graphs themselves in terms of slope (i.e. marginal cost and marginal revenue)

As can be seen in the graph above, the blue line depicts the cost and red line depicts the revenue. The break-even point indicates the point where revenue equals cost, i.e., the profit is zero. Beyond this point, additional production results in a net positive profit. In terms of slope, it is evident that the slope of revenue is greater than the slope of cost, indicating that marginal revenue exceeds marginal cost.

·       Graph the profit function on its own grid and mark and interpret the break-even point and its value on the graph

As seen above, the break-even point is where profit becomes zero.

·       Interpret the meaning of the graph of the profit function

The graph of the profit function shows the profit as a function of quantity manufactured. Hence, initially the profit is negative due to fixed setup (startup) costs. As the quantity increases, revenue starts to flow in and we reach break-even point, where revenue equals costs. Hence, profit is zero at this point and subsequent production results in positive profit.

(Part three)

For an actual company or start up, find out how many units are sold on a daily basis (for a hypothetical company, choose a number of units you would like to produce on a daily basis)

Let us assume that Peter manufactures 10 bearings per day. Hence, q = 10

·       Determine how many units of the product are produced on a daily basis (so q = n, where n is the number of units produced daily.  For instance, maybe n is 150, so q = 150 units)

q = 10

·       Plot the point of the number of units produced daily on the cost and revenue graphs

As can be seen above, daily production of 10 bearings corresponds to a revenue of $12,500 daily. Additionally, on the first day of month, the total cost to produce 10 units is $27,500, while the variable cost (only labor and material) is $2,500.

·       Determine the marginal cost for producing the nth unit (where q = n is the number of units produced on a daily basis. so, if n from above is 150 units, find the marginal cost for producing q = 150 units)

Marginal cost of producing the 10^th unit is $250 (basically the variable cost, since the fixed costs for setup have already been incurred at the beginning of month)

·       Find the average cost of producing the nth unit (where q = n is the number of units produced on a daily basis. so, if n from above is 150 units, find the average cost for producing q = 150 units)

The average cost of producing 10 units is the total cost divided by 10, hence we calculate it as follows:

Average cost =  = $2750

·       Graph the slope of the marginal cost of q = n and the slope of the average cost of q = n on the same grid

We can see above that at q = 10, the marginal cost curve has a positive slope, equal to 250 (the incremental cost of producing an additional unit), while the average cost curve has a negative slope (since as quantity of units produced increases, average cost decreases).

Then answer the following questions:

1)     Is the marginal revenue less than or greater than the marginal cost at q = n? Explain.

The marginal revenue is greater than marginal cost at q = 10, since the revenue for an additional bearing is $1,250 while the cost for producing an additional bearing is $250.

2)     Is the number of units sold daily (q =n) after or before the break-even point? What does this mean?

The number of units sold daily is before the break-even point, since we need to sell 25 bearings to reach break-even. So more bearings need to be produced beyond the 10 produced on day 1 to achieve the break-even point of 25 bearings.

3)     If production is increased by one extra quantity per day (i.e. if q = n + 1)) will the company continue to make money? Explain. (be sure to reference the formulas R(q + 1) – R(q) and C(q + 1) – C(q) in your explanation)

Yes, the company would continue to make money if production is increased to 11 bearings per day. In this scenario, the break-even would be reached sooner, since we are manufacturing more bearings daily.

R(q+1) – R(q) = R(11) – R(10) = 1250 X 11 – 1250 X 10 = $1,250

C(q+1) – C(q) = C(11) – C(10) = (25,000 + 250 X 11) – (25,000 + 250 X 10) = $250

Hence, on a daily basis the net profit increases by $1000.

4)     At q = n, does an increase of production increase or decrease the average cost for the company?

An increase in production decreases the average cost, as shown in the average cost graph above.

5)     Explain whether increasing or decreasing average costs would be better for the company.

Decreasing the average costs would certainly be better for the company, since lower the average cost, higher the profit.

(Part four)

1.     Provide an analysis of how you think the company will do over the next five years based on all of the information you have gathered from your experiment.

The company would do very well over the next five years, given that it only takes 2.5 days for the company to break even each month. Any subsequent bearings produced result in positive profit.

2.     In other words, explain whether or not you think the company will thrive, struggle, or tank within the next five years.  Give mathematical and economic/social reasoning for your explanations.

It is clear that the company would not only thrive, but prosper significantly, given the high value of profit. For example, each month (assuming 20 days working per month), the following applies:

Days needed for reaching break-even  = 2.5 (since 10 bearings are produced each day and 25 bearings are needed to achieve break-even).

Remaining number of days = 17.5

Net profit per month = 17.5 days after break-even X 10 bearings per day X $1000 profit per bearing after break-even = $175,000

Hence, the annual profit of the company is estimated as $175,000 X 12 = $2.1 Million