Question

In: Economics

4. Suppose Chipco produces memory chips for hand-held devices such as tablets and phones. Total costs...

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?

Solutions

Expert Solution

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

Rahul Sunny answered 3 years ago
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