In: Economics
4. Suppose Chipco produces memory chips for hand-held devices such as tablets and phones. Total costs in the short-run can be described with the following formula:
TC = 300 + 5Q + 0.1(Q2)
where Q is the number of chips produced per week and TC is the total cost of chips.
a. With the above cost function in mind, make a table of Q, TC, MC, AVC, and ATC at quantities 0, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100. (Hint: In Excel, suppose the Q cells are in column A, starting in row 1. The formula for the first cell of TC would be =300+5*A1+.1*A1^2)
b. If the firm competes in perfect competition and the price of these chips is $20, what is the profit-maximizing number of chips produced by Chipco? What is the profit? Show a graph of the firm (D, MR, MC, ATC) and depict the situation, including the profit box (you don’t need to plot points; just a general graph of the curves is fine).
c. If the price falls to $10, what is the profit-maximizing number of chips? What is profit?
We have been given the following information
Total Cost Function (TC) = 300 + 5Q + 0.1Q2
Average Total Cost Function (ATC) = TC/Q = (300/Q) + 5 + 0.1Q
Average Variable Cost Function (AVC) = 5 + 0.1Q
Marginal Cost Function (MC) = ?TC/?Q = 5 + 0.2Q
Quantity |
TC ($) |
MC ($) |
AVC ($) |
ATC ($) |
Price ($) |
0 |
300 |
5 |
5 |
-- |
20 |
10 |
360 |
7 |
6 |
36 |
20 |
20 |
440 |
9 |
7 |
22 |
20 |
30 |
540 |
11 |
8 |
18 |
20 |
40 |
660 |
13 |
9 |
17 |
20 |
50 |
800 |
15 |
10 |
16 |
20 |
60 |
960 |
17 |
11 |
16 |
20 |
70 |
1140 |
19 |
12 |
16 |
20 |
80 |
1340 |
21 |
13 |
17 |
20 |
90 |
1560 |
23 |
14 |
17 |
20 |
100 |
1800 |
25 |
15 |
18 |
20 |
Profit Maximization takes place at the point where the price is equal to the MC. From the above table we can see that at $20, the profit maximizing output is 80. The total cost is $1340.
Profit = Total Revenue – Total Cost
Total Revenue = Price × Quantity = 20 × 80 = $1600
Profit = $1,600 – $1,340
Profit = $260
Now it is given that the price has fallen to $10. At this price the equilibrium output is 30. Total cost is $540.
Profit = Total Revenue – Total Cost
Total Revenue = Price × Quantity = 10 × 30 = $300
Profit = $300 – $540
Profit = – ($240) Loss