Fall 2017 ECON 100 A Quiz: Homework #6 Time Remaining: 05:19:00 Submit Qulz This
ID: 1116114 • Letter: F
Question
Fall 2017 ECON 100 A Quiz: Homework #6 Time Remaining: 05:19:00 Submit Qulz This Question: 8 pts 3 of 5 (3 complete) This Quiz: 34 pts possible Suppose that the demand curve faced by a monopolist is given by P = 28-2Q and that the monopolist's cost function is C(Q) = 2Q2. The revenue function is thus given by R(Q)-(28-20)Q-28Q-2Q2. As in Homework #5, define MC (marginal cost) to be the cost of the NEXT unit of output, so that MC(Q) = C(Q+1)-C(Q). In other words, MC(3) = C(4)-C(3), and so on. Don't use calculus to compute MC, since you'll get the wrong answer below! Define MR (marginal revenue) in the same way, as the revenue from the NEXT unit of output. Thus, MR(Q) R(Q+1)- R(Q), so that MR(3) = R(4)-R(3), and so on. Given this information, fill in the following table (supplying a minus sign if needed): Q R(Q) MR(Q) C(Q) MC(Q) Using the MR = MC rule, the monopolist's profit-maximizing output is Q = | L . The revenue-maximizing output level is Q-I . At this output, profit |. At this output P =-and profitsExplanation / Answer
As per the given data,
P = 28-2Q ------ (1)
Multiplying equation 1 with Q to the both sides, will give revenue function.
R = 28Q -2Q^2
Cost function is:
C = 2Q^2
Q
R(Q) = 28Q-2Q^2
MR(Q)
C(Q) = 2Q^2
MC(Q)
Profit
0
0
0
0
1
26
26
2
2
24
2
48
22
8
6
40
3
66
18
18
10
48
4
80
14
32
14
48
5
90
10
50
18
40
6
96
6
72
22
24
7
98
2
98
26
0
8
96
-2
128
30
-32
As per the MR = MC,
The monopolist should produce the profit maximizing output = 4 units.
Because at this level of output, MR = MC = $14
At the output level of 4 units,
Price = 28-2*4
Price = $20
Profit = Revenue – cost = 20*4 – 2*4^2
Profit = $48
------
Revenue maximizing output level = 7 units ( it can be observed by the tabular data)
Profit at Revenue maximizing output level = 0
Q
R(Q) = 28Q-2Q^2
MR(Q)
C(Q) = 2Q^2
MC(Q)
Profit
0
0
0
0
1
26
26
2
2
24
2
48
22
8
6
40
3
66
18
18
10
48
4
80
14
32
14
48
5
90
10
50
18
40
6
96
6
72
22
24
7
98
2
98
26
0
8
96
-2
128
30
-32
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