# 1 - Todays Outline Isoquants Slope MRTS(marginal rate of...

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Today’s Outline: Isoquants Slope- MRTS (marginal rate of technical substitution) Curvature- elasticity of substitution Returns to Scale Isoquants help to visualize Long Run Today, we are studying attributes of production function These are all the combinations that will give an output of 6 Isoquant maps out combination of inputs that will give a certain output MRTS is the slope of an isoquant: indicates how one input can be substituted for another Similar to Econ 100A MRS (Marginal rate of substitution) of consumer theory, which measures consumers’ willingness to exchange one good for another If L increases by one unit, MRTS would equal to ΔK to keep q constant MRTS is always negative since isoquants are downward-sloping (trading off one input for another, moving in opposite directions) = =- MRTS dKdL MPLMPK = , q f L K =∂ ∂ +∂ ∂ dq f LdL f KdK How much quantity Δ How much quantity Δ when Δ a little bit of L when Δ a little bit of K At any point on the isoquant, = dq 0 =∂ ∂ +∂ ∂ 0 f LdL f KdK ∂ ∂ =∂ ∂ f LdL f KdK -∂ ∂ ∂ ∂ = f L f K dLdK - = MRTS MPLMPK Extreme examples: Leontif, fixed proportions, complements, MRTS definted Linear, substitutes Going to call this well shaped

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Leontif can’t trade off more: isoquant is just a dot Doesn’t have diminishing MRTS Linear case: MRTS constant, does not have diminishing MRTS Slope along line is constant Typically well-shaped isoquants will exhibit diminishing MRTS MRTS means getting less and less negative MRTS is steeper on the top Elasticity of substitution denoted by σ: Measures the curvature of the isoquant How does input ratio change when the MRTS Δ: = Input Ratio CapitalLabor =% ( ) σ Δ KL % = ( = ( ) × ΔMRTS d LK KLdMRTSMRTS d KL dMRTS MRTSKL When σ is high, MRTS is not changing much relative to KL KL can change a lot with little change to MRTS High σ means more substitutable On exams, you generally won’t lose points for the negative sign on MRTS Perfect Substitutes: Isoquant is flat MRTS is constant (no Δ) =∞ σ Isoquant is very curved: Low σ means MRTS Δ a lot relative to KL Perfect complements means = σ 0
Returns to Scale If we multiply all inputs by the same positive constant, we can classify the production functions to returns to scale:

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## This note was uploaded on 05/29/2011 for the course ECON 136 taught by Professor Betts,j during the Spring '08 term at UCSD.

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1 - Todays Outline Isoquants Slope MRTS(marginal rate of...

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