Blog 3 Miles VB

Marginal analysis

Miles's Kayak Manufacturing Shop 

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.)

Start up costs-  $30,000

Maintenance- $1,000

Utilities- $5,000

Supplies- $10,000

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

Each unit- $100 of polymers and hardwear per kayak

Salaries- $40,000

·       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)

R(q)= $1,200

·       Find the cost function

C(q)= $30,000 + $1000 + $5000 + $10,000 + $40,000 + $100(q)

·       Find the revenue function

R(q)= $1,200q

·       Find the profit function

P(q)= $1,200q – ($30,000 + $1000 + $5000 + $10,000 + $40,000 + $100(q))

·       Determine the break-even point value

About 69 kayaks

·      

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)

The break even point is where the cost and revenue curves intercept

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

·       Interpret the meaning of the graph of the profit function

The graph of the profit function has a lower slope than the revenue graph because the costs are subtracted from the slope. The graph starts at the break even point, which is the origin.

(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)

Q= 2

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

·       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) = $86,000 + 100(q)

So… the derivative is C’(q) = $100, which is the marginal cost of production for the additional item

·       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)

$100(2)/2 = $100 is the avg cost for making the 2^nd unit

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

 

Then answer the following questions:

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

Since the units sell for $1,200 each but only cost $100 to make, the marginal revenue is greater.

2)     Is the number of units sold daily (q =n) after or before the break-even point? What does this mean? Since only 2 units will be sold per day, and it takes 69 units to break even, q=n is well before the break even point.

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. This goes back to the company having a higher marginal revenue than a marginal cost. For instance, $1200(2+1) - $1200(2) = $1200

Is larger than $100(200 + 1) - $100 (2) = $100

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

Well since the marginal costs will remain at $100 per unit, it will not affect the average cost if they increase production.

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

Since decreasing average costs increases the profit margin of the revenue, it will be good for the company. This increases the efficiency of the company because with less costs they will make larger profits without having to necessarily increase outputs.

(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. 

Since the company will break even after selling only 69 kayaks, things are looking pretty good! This could be achieved in less than 35 work days. Since kayaks are very expensive items, but the plastic that it is made out of is not expensive in wholesale, this yields relatively high profit margins. Although the startup costs are high for the molding injection equipment, the high profit margins will provide returns after just a little while. If this shop was to make two kayaks a day for a year it would make:   ($2400 x 365) – 86,000 = $790,000.

Obviously a small shop wouldn’t want to make kayaks every day of the year. But just from the fact that 35 work days would cause the shop to break even, it is evident that this shop would thrive if placed in an area where kayaking was prevalent. 69 kayaks is not a difficult number to reach in areas of the USA.

2.