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Lecture

# Classroom Lecture Notes - Kings

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Western University

Economics

Economics 2150A/B

Hugh Cassidy

Fall

Description

2 3
Example TC(Q) = 100Q – Q + 3Q
2 3
TVC = 100Q – Q + 3Q all are variable in this case
TFC = 0 none in this case
AC (Q) = TC/Q = 100Q – Q + 3Q /Q = 100 – Q + 3Q 2
2 3 2
AVC = TVC/Q = 100Q – Q + 3Q /Q = 100 – Q + 3Q
AFC = TFC/Q = 0
AC = AVC + AFC
MC(Q) = ∆TC(Q)/ ∆Q = dTC/dQ = 100 – 2Q + 9Q 2
Example 2
3
TC(Q) = 50 + 8Q + Q
TVC(Q) = 8Q + Q 3 AVC(Q) = 8Q + Q /Q = 8 + Q 2
TFC(Q) = 50 AFC = 50/Q
2
AC = AVC + AFC = 50/Q + 8 + Q
2
MC(Q) = TVC or TC doesn’t matter = 8 + 3Q
Short-run vs Long-run
Long-run
- Firm can vary all inputs
- All costs are variable
- TC = TVC
Short-run
- One input is fixed
- STC is the sum of TVC + TFC Marginal Cost and Average Cost
When MC > AC
- AC is rising
When MC < AC
- AC is falling
When MC = AC
- AC is constant
Figures 8.16 & 8.9 in textbook for short run and long run respectively
In the Long-run: MC crosses AC at the minimum of AC
In the short-run: SMC crosses the SAC and AVC at their minimum
Solving for Total Cost Curve (Long-run)
TC = wL + rK
Solve for L* and K* as functions of Q
Then Substitute into TC = wL + rK
- TC (Q) Total cost as a function of only Q
Cobb-Douglas
1/2 1/2 -1/2 1/2 1/2 -1/2
Q = 3L K w = 1, r = 4 solve for TC(Q) MPL = 3/2L K MPK = 3/2L K
1) MRTS = MPL/MPK = K/L
Set equal to w/r = ¼
K/L = ¼ L = 4K
1/2 1/2
2) Substitute L = 4K into Q = 3L K
Q = 3(4K) K/2 1/= 6K
K = Q/6
L = 4K = 4Q/6 = 2Q/3
3) TC = wL + rK = L + 4K
2/3Q + 4(Q/6) = 4/3Q
AC = TC/Q = 4/3Q / Q = 4/3 MC = ∆TC/∆Q = 4/3
Perfect Substitutes
Q = 2L + 4K MPL = 2, MPK = 4
1) w = 1, r = 3 MPL/w = 2/1 > MPK = 4/3 K* = 0
Substitute Q = 2L + 4(0) L* = Q/2
TC = wL + rK = L + 3K
TC = Q/2 AC = 1/2 MC = 1/2
2) w = 1, r = 1 MPL/w = 2/1 < MPK = 4/1 L* = 0
Substitute Q = 2(0) + 4K K* = Q/4
TC = wL + rK = 1(0) + 1(Q/4)
TC = Q/4
3) w = 1, r = 2 MPL/w = 2/1 = MPK/r = 4/2 = 2
- Any (L,K) bundle is optimal
- Say K = 0, Q = 2L + 4(0) = L = Q/2
TC = 1(Q/2) + 4(0) = Q/2
Perfect Compliments
Q = min{2L,4K} w= 2, r = 1
Opti

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