Answers to Homework

Chapter 11

4.  a. 

Q_E = 4,000,000 - 100 P_E  => 100  P_E  = 4,000,000 - Q_E => P_E  = 40,000 - 0.01 Q_E

TR_E = P_E  * Q_E = (40,000 - 0.01 Q_E) * Q_E = 40,000 Q_E - 0.01 Q_E ²

MR_E = d TR_E / d Q_E = 40,000 - 0.02 Q_E

MR_E = MC => 40,000 - 0.02 Q_E = 20,000 => 20,000 = 0.02 Q_E => Q_E = 1,000,000

P_E  = 40,000 - 0.01 (1,000,000) = 30,000

.

Q_U = 1,000,000 - 20 P_U  => 20  P_U  = 1,000,000 - Q_U => P_U  = 50,000 - 0.05 Q_U

TR_U = P_U  * Q_U = (50,000 - 0.05 Q_U) * Q_U = 50,000 Q_U - 0.05 Q_U ²

MR_U = d TR_U / d Q_U = 50,000 - 0.10 Q_U

MR_U = MC => 50,000 - 0.10 Q_U = 20,000 => 30,000 = 0.10 Q_U => Q_U = 300,000

P_U  = 50,000 - 0.05 (300,000) = 35,000

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Chapter 14

10. 

a.

q = 8 L ^1/2 => MP_L = d q / d L = 4 L ^-1/2

MRP_L = MP_L * MR = (4 L ^-1/2 ) * 150 = 600 L ^-1/2

Profit maximization => MRP_L = W => 600 L ^-1/2 = 75 => 8 = L ^1/2 => L = 64

.

b.

q = 8 (64 ^1/2 ) = 64

.

c.

π = TR - TC = P * Q - w * L = (150 * 64) - (75 * 64) = 4,800