You are given the following data for your firm, which sells high-capacity video

Question

You are given the following data for your firm, which sells high-capacity video MP3 players.

Question 1

Which of the following represents the correct formulas for PP and MRMR in terms of QDQD?

Select one:

a. P=500.05QDP=500.05QD ; MR=500.1QDMR=500.1QD

b. P=100020QDP=100020QD ; MR=100040QDMR=100040QD

c. P=20+1000QDP=20+1000QD ; MR=40+1000QDMR=40+1000QD

d. P=100010QDP=100010QD ; MR=1000QD20QD2MR=1000QD20QD2

Question 2

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Which of the following equations is correct, based on the data above?

Select one:

a. ATC=Q23Q+536+1500QATC=Q23Q+536+1500Q

b. MC=0.5Q21.5Q+268MC=0.5Q21.5Q+268

c. AVC=Q29Q+536Q+1500AVC=Q29Q+536Q+1500

d. AVC=Q33Q2+536Q+1500QAVC=Q33Q2+536Q+1500Q

Question 3

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The profit-maximizing quantity occurs at _______ and the profit-maximizing price occurs at _________.

(Since MC is in terms of Q2Q2, solving with calculus and algebra can be messy. Your table should give an exact answer.)

Select one:

a. Q=14Q=14; P=$720P=$720

b. Q=12Q=12; P=$760P=$760

c. Q=8Q=8; P=$840P=$840

d. Q=6Q=6; P=$880P=$880

Question 4

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How much total profit would your firm earn if you set PP and QQ at their profit-maximizing levels?

Select one:

a. $612

b. $6,108

c. $6,720

d. $840

Question 5

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Describe the competitiveness of the market by calculating the Lerner index.

Select one:

a. 19.0%

b. 23.5%

c. 8.74%

d. 3.12%

Q P TC 0 $1,000 $1,500 2 $960 $2,568 4 $920 $3,660 6 $880 $4,824 8 $840 $6,108 10 $800 $7,560 12 $760 $9,228 14 $720 $11,160 16 $680 $13,404 18 $640 $16,008 20 $600 $19,020

Explanation / Answer

1)

Option b is correct

P = 1000 - 20Qd

MR = d(PQ)/dQ = 1000 - 40Qd

2)

Option a is correct

ATC = Q2 - 3Q + 536 + 1500/Q

3)

Profit would be maximized where MR = MC

MC = d(TC)/dQ = 3Q2 -6Q + 536

MR = 1000 - 40Q

1000 - 40Q = 3Q2 -6Q + 536

3Q2 +34Q -464 = 0

Q = 8 and P = 840 (Option c)

4)

Profit earned = P x Q - TC = (840 x 8 - 6108) =$612 (Option a)

5)

Lerner index = (P - MC)/P

MC = 3Q2 - 6Q + 536 = 680

Lerner index = (840 - 680)/840 = 19% (option a)

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