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Lecture13

# Lecture13 - Lecture 13 Isocost curves and optimal...

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Lecture 13 Isocost curves and optimal production Opportunity cost and sunk cost Fixed costs, variable costs, sunk costs Average and marginal costs More on cost minimization

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Substituting inputs: the marginal rate of technical substitution MRTS = change in capital/change in labor for a fixed level of output = - ∆K/∆L (for fixed q) Labor Capital ∆K ∆L ( - 1)*Slope of tangent line
Isocost curves rK + wL = C where r and w are the annual costs of capital and labor Labor Capital rK+wL =C 2 rK+wL =C 1 K=( - w/r)L+C 2 slope of isocost curve is ( - w/r) K=( - w/r)L+C 1

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Minimum production cost Minimum cost production for Q 1 is C 1 : Labor Capital rK+wL =C 1 q(L,K)=Q 1 K* L*
Isocost and isoquants Marginal Rate of Technical Substitution = ( - 1)*slope of tangent line to the isoquant; hence at cost -minimizing production, 𝑀𝑀𝑀𝑀 = 𝜕𝜕 𝜕𝜕 𝜕𝜕 𝜕𝜕 = 𝑀𝑀 𝜕 𝑀𝑀 𝜕 = −𝑤 𝑟 Labor Capital rK+wL =C 1 q(L,K)=Q 1 K* L*

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Minimizing costs for different levels of production Labor Capital rK+wL =C 2 rK+wL =C 1 q(L,K)=Q 1 q(L,K)=Q 2
Expansion path for least-cost production Labor Capital rK+wL =C 2 rK+wL =C 1 q(L,K)=Q 1 q(L,K)=Q 2

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Long-run total cost C=100 C=200 Q=50 Q=10 C=100 C=200 Q=15 Q=10 Output Total Cost 200 100 10 20 50
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