Blog Post 3

(Part one)

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

(Part two)

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.)

                  -Produces rubber ducks for 10cents/unit

                  -Sell for $10/unit

                  -Targeting young children

                  - History involves law suits with chemicals found in plastic in the past, but have moved                                       past it and are back on track with a healthier/safer product line

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.)

                           Factory & Equipment                         $1million

                           Maintenance                                         $1,000

                           Utility Bills                                               $10,000

                           Supplies                                                      $100,000

                                             Total $1,111,000                                                  

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

                           Each Unit $0.10/unit

·       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) = 250(q)

                           Selling price for 1 unit: $10

·       Find the cost function

                           C(q)= $,1,111,000 + $0.10(q)

·       Find the revenue function

                           R(q)= $10(q)

·       Find the profit function

                           P(q)= 10(q) – (1,111,000 + 0.10(q))

                           P(q)= -1109020

·       Determine the break-even point value

                           Break Even: $10(q) = $1,111,000 + $0.10(q)

                                                     $9.9(q) = $1,111,000

                                                     (q) = 112,222

·       Graph the cost function and the revenue function on the same grid and mark the break-even point and its value on the graph (Dot is break-even point & please count x-axis as horizontal and aligned with y-axis at origin--- computer error)

·       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)

                           At that point profits are exactly equal to the cost of producing the good. The marginal                                        revenue increases more quickly than the marginal cost since the selling price is higher                                                   than the cost of production.

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

                           At the break even point profits will begin to be made.

·       Interpret the meaning of the graph of the profit function

                                    From the graph we can see that I will not be making a profit for a long time before I                                               reach break-even point.

(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)

·       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)

                           Number of units produced daily: 200

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

                           *See the cost and revenue function graph

·       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)

                           C(q)= $1,111,000 + $0.10(q) => C’(q)= $0.10

                           Used derivative to find that the marginal cost of production is $0.10 because that is                                             how much it costs to produce each additional item (slope of line)

·       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)

                                             $0.10(200)/200

                                             $0.10 is the average cost of producing the 200^th unit      

·       Graph the slopes of the marginal cost of q = n and the average cost of q = n on the same grid point and its value on the graph.

Then answer the following questions:

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

The marginal revenue is greater than the marginal cost because the line is steeper due to the cost of production only being $0.10 while the selling price is $10.

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 is long before the break-even point. This means that there will be no being made for a very long time.

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 will continue to have higher marginal revenue than marginal cost.

This is because $10(200 + 1) – $10(200)= 2010 – 2000 = $10. AND $0.10(200 + 1) – $0.10(200) = 20.1 – 20 = $0.10

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

Since we have shown that the marginal cost will always be $0.10, no matter what the amount produced is, an increase in production will not affect the average cost for the company.

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

If the average costs went up, this would cut into the revenue for the company and therefore affect the profitability. In other words, it will always be better for a company to decrease average costs.

(Part four)

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.  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.

Break-even is at quantity 112,222. Therefore, with the company being able to produce 73000 (200x365) units a year, the company will begin to produce profits. in year 2. However, the startup costs will not be covered for another year since the revenue will be 730,000/year with 1,111,000 in startup costs to cover. Since this is a company that produce rubber ducks, I do not think there will be enough capital supplied to keep the company running until all the initial difficulties are overcome. As a result, I believe the company will fail.