ECN 520

Test 2 - ANSWERS

1.

a. MRTSLK = ( Q/ L)/( Q/ K) = 7.5L-0.25K0.25/2.5L0.75K-.25 = 3K/L

= 3K/L = PL/PK = 2 => L = 1.5K b.   100 = 10L0.75K0.25

10 = (1.5K)0.75K0.25 = 1.36K

Thus, K = 7.35; L = 11.03; TC = 588

c. Click to see graph.

2.

  1. AVC = TVC/Q = 50 + 10Q; Shutdown Price = 50
  2. Set P = MC

    3. 75 = 50 + 20Q;

    Q = 1.25

  3. Set P = MC
P = 50 + 20Q

Q = -2.5 + 0.05P

" P >= 50

 3.
  1. LAC / Q = -4 + 0,004Q;

    2. \ Q = 1000

    Min LAC = 500; Thus P = 500

  2. With P below the minimum LAC, there will be exit and rising prices until P hits $500.
  3. N = 72,000/ 1000 = 72
4.
  1. QD = QS => P = 10; Q = 40;

    2.  

  2. P = MC

    3. 10 = 2 + 2Q; Q = 4; p = 0

  3. QS' = 5P - 20
Set QD = QS'

P = 11.4; Q = 37.2

Click to see graph.

 5.
  1. MR = MC => 10,000 - 10Q = 2,000

    2. Q = 80; P = 6,000

  2. NONE
  3. PC = 2,000 => QC = 1,600
W.L. = 0.5(800)(4,000) = 1,600,000

Click to see graph.

 6.
  1. P = 5 => Q = 2,000

    2. MR = 9 - 0.004Q = 1 when Q = 2,000

    LTC = 7Q - 0.004Q2 + 0.000001Q3

    LMC = 7 - 0.008Q + 0.000003Q2 = 3 when Q = 2,000

    : Reduce Output and Raise Price

  2. P/ Q = LAC/ Q
-0.02 = -0.04 + 0.000002Q

Q = 1,000

 : AC = P = 4

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