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Economics (934)
Lecture

# Classroom Lecture Notes - Kings

6 Pages
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School
Western University
Department
Economics
Course
Economics 2150A/B
Professor
Hugh Cassidy
Semester
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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