Answer key

 

  1. B
  2. E
  3. A
  4. D
  5. B
  6. D
  7. A
  8. A
  9. E
  10. C
  11. C
  12. A
  13. C
  14. C
  15. B
  16. C
  17. B
  18. A
  19. D
  20. B

 

21.  Quantity of Variable Input     Total Output   Marginal Product        Average Product

 

0                                                          0                      --                                  --

1                                                          50                    50                                50

2                                                          80                    30                                40

3                                                          90                    10                                30

4                                                          96                    6                                  24

5                                                          100                  4                                  20

6                                                          96                    -4                                 16

 

22.  If the firm is minimizing its costs of production, then the MRTS will equal a ratio of prices of inputs.

 

The ratio of prices PK/PL = 50/5 = 10 and the MRTS for labor MPK/MPL = 12

Since these two ratios are not equal, the firm should change the mix of inputs.  It should use more capital and less labor to make the ratios equal.

 

 

  1. To determine the optimal output level, we first equate MC to P. That is, MC = 50q/10 = P ↔q = 50

AVC = 25q/K = 125.  Since P > AVC, Spacely will maximize profits at 50 units.  Its profits are:

Pq – C(q, 10) = 6100.

 

24.  Fist set quantity demanded equal to quantity supplied to solve for equilibrium price.

P = 30.  At this price, equilibrium quantity will be 80,000.  The lowest price such that no units are bought and sold is $50 (set QD = 0 and solve for P).

CS = ½(50-30) 80000 = 800000. 

PS = 30 (20000) + ½(80000-2000)30 = 1,500,000.  If price ceiling of $15, producers will only supply 50,000 units to the market.

CS’ = ½(50000)(50-37.5)  + 50000 (37.5 – 15) = 1437500.

PS’ = 20000(15) + ½(50000-20000)15 = 525000.  In this example consumer surplus has risen by 637500.  However, not all consumers are better off as the price ceiling results in a shortage.  Some of them are willing to pay $15 for cable TV but cannot get it.  Producer surplus decreases by 65% due to the price ceiling.  Producers are worse off.

 

  1. a. First calculate the price elasticity of demand:

ED = (ΔQ/ΔP)(P/Q)

            Solve Q in terms of P to find ΔQ/ΔP

                        Q = 250- 0.5P

                        ΔQ/ΔP = -0.5; ED = -0.5 (300/100) = -1.5

                        MR = P + P(1/ ED)

                        MR = 300 + 300 (1/-1.5) = 300 -200 = 100

 

b. If MC = 0, the firm is not maximizing profit since MR should be equal to MC.  The firm should expand output.

            MR = 500 – 4Q = 0

            4Q = 500

            Q = 125

26.  To determine optimal prices MRA = MRB = MC.

Setting MRB = MC

70 – 0.001QB = 10

-0.001 QB = -60

QB = 60000

PB = 70 – 0.0005(60000) = $40

Setting MRP = MC

20 – 0.0004QP = 10

-0.0004 QP = -10

QP = 25000

PP = 20 – 0.0002(25000) = $15

 

PB = $40; PP = $15.  Therefore the prices are not optimal.