Mishal Alotaibi

                                            

                   

PART 1

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

                                                                                   

           

                                                                                   PART 2

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.)

Xpyne is a phone manufacturing company which is located in Cape Town, South Africa. It specializes in the manufacture of smartphones and offering custom production for large companies. The smartphones produced by the company run on an android operating system 5.0 lollipop or commonly referred to as android L.  The company was launched by Edwins Naminaque in 2004 March to offer the natives and other individuals in Southern and central Africa access to quality gadgets at an affordable price. The company’s earnings have increased steadily and it has gained popularity to other parts of Africa and the world in general. A recent study done by Synovate Africa has revealed that one out of 300 Africans uses an Xpyne device. The company has a target of selling its devices in Europe and Asia as from the next financial year.

Then, determine the following:

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

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

·      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)

·      Find the cost function

·      Find the revenue function

·      Find the profit function

·      Determine the break-even point value

·      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)

·      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

Fixed costs

 The company has fixed costs of approximately $12000 per day. This consists of $7000 supplies, $1000 heating costs, $3000 internet costs and $1000 rent.

Variable costs

In order to successfully produce one device, the company spends approximately $100. It then sells the device at $180 to the retailers who can then sell to the consumers at prices dependent on location and other factors.

The cost function for the production is equal to the fixed costs + variable costs

= 12000 + 100q

The revenue function will be equal to price * quantity

= 180q

The profit function will be equal to Total revenue – The total cost.

 = 180q – (12000 + 100q)

Break- even value

 This occurs when total revenue = total cost

Thus; 180q = 12000 + 100q

80q = 12000

Q = 150

The revenue = p* q

 = 180 * 150

= 27000

Thus break even value = $27000

A graph showing the break- even point, revenue and the cost functions.

Assuming that 100 is the number of items produced, we come up with the following graphical representation.

Graph showing the break-even point, revenue and cost functions

 

                                                                                                            The revenue function

27000

12000                                 Break-even point

                                                                                                                               Cost function

                                 Quantity of smartphones                      150                                          200

                                                                                       

 The break- even point on the graph is a point where the total revenue = total cost (TR = TC)

It is a point below which a company will make a loss and above which it will make a profit.

It is the point of intersection of the Revenue and cost function on the graph.

The profit function graph:

                        Break-even point                                             Revenue function

                                                                                                                                    Cost function

27000

12000                                                                                                           profit function

                                                                                           100

-12000

                                                                                                           

Explaining the profit function:

The profit function shows the profits that the company makes with respect to the quantity produced and at the given price level. Profits are accrued at 100 smartphones.

PART 3

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)

·      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)

·      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)

·      Graph the slope of the marginal cost of q = n and the slope of 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.

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

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)

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

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

Marginal cost for producing 200 units:

The company incurs a cost of $150 * 100

= $15000

Thus total cost = 12000 + 15000

= 27000

Average cost of producing 150 smartphones:

(27000 /150)

= $180

To produce 200 units, the cost will amount to:

Fixed costs + (200 * 100)

= 12000 + 20000

= $32000

The cost of producing (200 -150) units is:

32000 – 27000

= $5000

The marginal cost is the cost of producing one extra unit thus:

Marginal cost = (5000/50)

= 100

Graph of Average cost and Marginal cost

 

                                                            Average cost

180

                                                                  Marginal cost

100

                                             No of smartphones produced                150

Is the marginal revenue greater than the marginal cost at q=n? Why?

The marginal revenue is greater in value than the marginal cost at the point q =n. This is because any additional production does not increase the production costs.

The company will still operate comfortably because the revenue is greater in value than the costs incurred.

Will the company still make profit if they increased their productions?

The cost of manufacturing 150 smartphones is $27000

The cost of manufacturing 151 smartphones = $27100

Extra cost incurred = $100

Revenue from selling 150smartphones = 150 * 180

= 27000

Revenue from selling 151 smartphones = $27180

The extra revenue realized = $180

Thus profit = 180 – 100

= $80.

Conclusion: The Company will increase the amount of profit if they increase production.

Does average production cost decrease with increased production?

The average cost for producing 150 smartphones is $27000 / 150

= $180

The average cost of producing 151 smartphones is 27100 / 151

= $179.470

Therefore, an increase in the quantity of smartphones produced decreases the average cost of production significantly I.e. (180 – 179.470 = $0.53)

                                                       PART 4

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. 

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.

An analysis on whether the company will thrive in the next 5 years

The company will thrive in the next five years. This is because currently they are making profit with the number of smartphones they are currently producing and at the given price level.

Profit = Total revenue – total cost.

For the necessary profit maximization condition, TR = TC

Given 150 units each incurring $100 to produce with a fixed cost of $12000

TC = 12000 + (150 *180)

= 27000

TR = 150 * 180

= 27000

Thus the necessary condition for profit maximization has been satisfied.

The profits will increase significantly if they increase the number of units they are producing since it will lower the average costs while increasing the amount of profit.

With every extra unit produced, a profit of $80 is realized.

Consequently,

An increase in the quantity of smartphones produced decreases the average cost of production significantly I.e. (180 – 179.470 = $0.53)