Jeffrey Williams' Marginal Analysis

Part 2)
C) Crown, Cork, & Seal Co. manufactures metal cans for food and beverage companies such as Coca Cola Co. and Pepsi Co.  CC&S was founded in 1903 in Trenton, New Jersey.

Fixed Cost:
     Utilities - $20,000
     Supplies - $5,000
     Fixed Sales & Administration - $6,500
     Insurance - $10,000
Total Fixed Costs - $41,500

Variable Cost: $0.40/can

Price: $0.80/can

Cost Function: C(q) = 0.40x -41,500

Revenue Function: R(q) = .80x

Profit Function: P(q) = .40x - 41,500

Break Even Value: 0 = .40x - 41,500 or C(q) = R(q); x=103,750 cans

The break-even point is where costs equal to revenues (C(q)=R(q)).  In this case, the break-even point is at 103,750 cans at which point both costs and revenue will be $83,000 resulting in a profit of $0.00 also know as breaking-even.

On the graph, the break-even point ((103,750,83,000)) is the point at which the revenue function crosses the cost function.  The reason why the two functions cross is that the revenue function has a larger slope than the slope of the cost function.

The break-even point is at (103,750, 0).  This means that after producing the 103,750th can, all the company's fixed costs are covered and its profit is $0.00.

The graph of the profit function shows the amount of profit (Revenue- Expenses) that the company makes on each can.  

Part 3)

Crown, Cork, & Seal produces 50,000 can per day.

The marginal cost for producing each can past the 50,000th can is $0.40.

The average cost for producing 50,000 cans is $1.23 per can.

1) The marginal revenue is greater than marginal cost because the revenue function, due to its larger slope a.k.a marginal revenue, eventually surpasses the cost function on the Revenue v. Cost graph in Part 2.  

2)  The number of units sold daily before the break even point are units which contribute all of their revenue to covering the fixed costs of production and the marginal cost of their production.  Units produced after the break even point have revenues that contribute to profit less variable cost.  

3)  Yes. because the cost to produce one extra unit is less than the revenue that the unit generates for CC&S.  

R(50,001)-R(50,000) = .80                                          C(50,001)-C(50,000) = .40

4) At q=50,000, an increase in production decreases the average cost for the company.

Average Cost at q=50,000 is $1.23

Average Cost at q=100,000 is $.815

5) The company would benefit from decreasing average cost since a lower average cost means that each unit is cheaper to make. 

Part 4)

1) Based on this experiment, I feel that Crown, Cork, & Seal Co. will be profitable over the next five years as long as the company can produce and sell more than 103,750 cans.

2) I think that CC&S will thrive thrive in the next five years since the company's marginal costs are less than its marginal revenue so a profit is made on each can sold.  Also, Coca Cola is moving towards using more of its new aluminum cans for its soda which means that CC&S could see an increase in demand for cans.