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Profit Max

Hello,

I have attached some HW problems that I need help on.

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P1 - Price/Output Determination. Cold Case, Inc., produces beverage containers used by fast food franchises. This is a perfectly competitive market. The following relation exists between the firm's beverage container output per hour and total production costs:

Total Output Total Cost
0 $35
1,000 85
2,000 145
3,000 215
4,000 295
5,000 385
6,000 485
7,000 610

A. Construct a table showing the marginal cost of paper cup production.
Total Output Total Cost Marginal Cost
0 $35
1,000 85 $50
2,000 145 $60
3,000 215 $70
4,000 295 $80
5,000 385 $90
6,000 485 $100
7,000 610 $125

B. What is the minimum price necessary for the company to supply one thousand cups?
The total cost for producing 1000 cups is $85. So the company should keep minimum price of cups at $85 per thousand.

(Remember in a competitive market, price = marginal revenue.)
C. How many cups would the company supply at industry prices of $75 and $100 per thousand?
For profit maximization, the firm should produce at MC=MR, in a competitive market MR=P
When P=MR=$75
The MC increases as firm increase the total output, at 3000 units the MC is $70 and at 4000 units the MC is $80. So the firm should produce and sell 3000 units.
Profits = 3000*75/1000-215=$10

When P=MR=$100
The MC increases as firm increase the total output. MC is exactly equal to $100 at 6000 units. So the firm should produce and sell 3000 units.
Profits = 6000*100/1000-485=$115

P2 - Price/Output Determination. The accompanying graph summarizes the demand and
costs for a firm that operates in a perfectly competitive market.

Price

48
46
44
42 ATC
40
38
36
34
32
30
28 MR
26
24
22 AVC
20
18
16
14
12 AFC
10
8
6
4
2
0
1 2 3 4 5 6 7 8 9 10
Quantity
a. What level of output should this firm produce in the short run?
In the short run firm should produce as long as the MC<MR. The MC curve passes the MR curve between 6 and 7 units. Thus, the firm should produce 6 units.

b. What price should this firm charge ...

$2.19