Blog Post 3

Part 1

The Pink Panther Hypothetical Company

The Pink Panther Hypothetical Company (PPHC) was founded on June 28^th 1855 by seven courageous and visionary entrepreneurs who were ahead of their time. The company is based in Illinois and sells goods including stuffed animals, memorabilia and apparel. The company produces all of its products, which helps keep the company’s cost low. Moreover, the company’s targeted demographics include teenagers and younger adults. There is no targeted geographic location because its storied history has helped make the company ubiquitous throughout the nation.  

Part 2

·      Total Fixed Costs: $10,000

o   Utilities: $1000

o   Rent: $2000

o   Supplies: $3000

o   Insurance: $1000

o   Equipment: $3000

·      Variable Costs: $5

o   Transportation: $2

o   Commission: $2

o   Damages: $1

Sale price: $10

Cost Function: C(q)= 5(Q) + 10,000

Revenue Function: R(q)= 10(Q)

Profit Function: P(q) = 10(q) – (5(q) +10,000) = 5(q)

·      Break-even point value:

o   Revenue=Cost

o   R(Q)=C(Q)

Break-even point = 5Q+10,000=10Q = 2000 Units

The break-even point on the graph is at 2000 units sold and $20,000 in revenue. At this point, the company has covered the initial costs of starting the business as well as the variable cost of producing the number of goods it has sold. And units sold after this point would result in a profit for the company and any units sold less would result in a loss for the company. In the graph, the revenue function has a much steeper graph and starts at 0, while the cost function’s slope is much less steep but starts at 10,000. Because the slope for the revenue function is steeper, it allows the company to eventually mitigate the initial costs and to make a profit. In terms of marginal costs and marginal revenue, it basically represents how much money the company will get or will have to pay for producing or selling one additional unit. At this point in the graph, the slopes represent a steady linear growth and each additional unit sold will still amount to $10 and the cost to make an additional unit is still $5.

 

Part 3

Units produced daily = 150 N=Q Q=150

Marginal Cost (MC) = C’(q)

It will cost the company 5 dollars to produce nth unit for the PPHC

C’ (q) = (5q)’ + (10,000)’

C’ (q)= MC = $5

Average Cost = Cost/# of units sold

5(Q) + 10,000/150 = $71.667

It cost an average of $71.667 to produce 150^th unit.

Questions to answer

-The marginal revenue is greater than the marginal cost because each unit is still sold for $5 while the cost is $3

- Assuming the company sells every unit it sells, the company should break even on the 14^th day because it produces 150 units a day and needs to sell 20,000 units to break even.

-Yes, if the company increases production by unit daily, the company’s profit margin will continue to grow because the company still sells each unit for more than it costs to make one unit. Using the formula (q + 1) – R(q) we can see that the revenue will continue to increase, because the marginal revenue remains $5. Also, the marginal cost formula C(q + 1) – C(q)  tells us that the cost will stay at $3.

-At q=n, if the company produces additional units, it decreases the average cost of producing an item. For example, if the company sells 151 units instead of 150, the average cost would be $71.225 instead of $71.667

-Decreasing average costs would be a clear benefit for a company because it would result in larger profit margins. Until the breaking point, the company is still trying to cover the initial costs and every unit becomes increasingly cheaper to produce until the breaking point is reached.

Part 4

Based on the analysis of the company, over the next five years, the company should see rapid growth. The reason is because the company has a high profit margin. That is, the company is selling its products for much more than it costs to produce each unit. Moreover, the company produces a substantial amount of units daily, which also translates into profits and hopefully growth for the company.

Surely, the company will thrive because if it produces 150 units a day it will produce 54,750 in a year, while it only needs to sell 20,000 units to break even. This means the company will realize large profits.