Blog Post 3 Maria Jose

Blog Post #3

Part 1

The company I will be speaking about will be a hypothetical company that sells personalized cellphone covers. It is a small company near American University, which opened in 2014 and has expanded its popularity amongst students mainly. Their target demographic is teens and young adults, between 15 years old and 25 years old. However, they have all types of cellphone covers so anyone with a cellphone would be a target demographic for this company. The company began when a student noticed there was a big demand for personalized cell phone covers where people would choose a drawing or make their own drawing and want it as they cover. With this increase in demand for personalized cover this student decided to open this small company in which people could send what they wanted as a cover and they would make it. People could order it online or through telephone and they are delivered. The cover would be made in one week, but they also sale already made covers online.

Part 2

Start up cost:

·      Equipment: $850

·      Utilities: $400

·      Total: $1250

Variable costs: $17

Price per unit: $30

R(q)=30q

C(q)=17q+1250

P(q)= (30q) – (17q+1250)

Break-even point:

30q=17q+1250

13q=1250

q=96.15

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

Interpretation of the meaning of the break-even point: the breakeven point would be the point where you will start earning profit with every new cellphone cover sold. For the 97^th cover sold the company will have paid the start up cost of the company and will start earning profit money.

Interpretation of the graphs in terms of slope (marginal cost and marginal revenue):

The revenue function has a steeper slope than the cost function throughout the graph, meaning the company will ultimately win more revenue than cost after a time. When more cellphone covers are produced after the breakeven point the marginal revenue will be surpassing the marginal cost.

Graph: profit function + mark and interpret break even point and its value

Interpretation of the meaning of the graph of profit function:

The breakeven point is when the profit function goes through the x axis. Meaning that before this point, before selling over 96 covers the company was actually losing money not winning; however, after the 96^th cover the company starts winning money.

Part 3

How many units are sold on a daily basis: q= $10 covers

Determine marginal cost for producing the nth unit: $17

Average cost for producing nth unit:

(17(10) + 1250)/10= $142

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

Answer:

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

At q=10 my marginal revenue would be greater than my marginal cost. The marginal revenue would be 30 and my marginal cost would be 17. It is greater because in order to gain profit the marginal revenue should be greater than the marginal cost.

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

It is before the break-even point, which is $96.15. This means when the company starts it will be losing money, not earning right away; however when the company reaches the breakeven point it will start making profits.

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 it will continue to make money. Doing R(q+1)-R(q) will give you the value of:

            30(11)-30(10)= 330-300= $30 ; meaning that MR at q+1=30

Moreover for C(q+1)-C(q) will give you the value of:

            [17(11)+1250]-[17(10)+1250]= $17 ; meaning that MC  at q+1=17

One knows that it will end up winning money because the MR-MC will give my company a value of $13, which is the profit.

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

An increase in production increases the average cost; however in the long run you would have more benefit after you reach the break-even point.

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

Increasing the average cost would be worst for the company, so we are better off decreasing the average cost that way we can spend less money and earn more, having a longer profit.

Part 4

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.

Over the next five years the company seems like it would do extremely well, given that the start up cost to do the company wasn’t that much and what it costs to make one cover isn’t that expensive. We can see the company would recover what it spent and start ending profit before the end of the first year working. However, to keep its success it should keep on selling the amount it is daily and more. From the looks of it will thrive and maybe on the long run it will consider expanding. A mathematical explanation to why it would thrive in the next five years is the profit function graph where we can see it is positive (meaning gaining money) before the first year of operation.