# Lecture 11 - Lecture 11 Production II When thou cuttest...

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Lecture 11 Production II When thou cuttest down thine harvest in thy field, and hast forgot a sheaf in the field, thou shalt not go again to fetch it: it shall be for the stranger, for the fatherless, and for the widow: that the LORD thy God may bless thee in all the work of thine hands. When thou beatest thine olive tree, thou shalt not go over the boughs again: it shall be for the stranger, for the fatherless, and for the widow. When thou gatherest the grapes of thy vineyard, thou shalt not glean it afterward: it shall be for the stranger, for the fatherless, and for the widow. Deuteronomy 24:19-21 The Economics Outline 1. Diminishing RTS 2. Cross Productivity Effects 3. Returns to Scale 4. Four Production Functions 5. Output Elasticity w.r.t. an Input The Mathematics Outline 1. Some Calculus and Algebra 2. Homogeneity Diminishing Marginal Rate of Technical Substitution Last time we developed concept of the RTS L,K with the following definition: K L K L q q K L f f MP MP dL dK RTS = = = = 0 , Looking at how RTS L,K changes as we move along the isoquant, we consider the following equation: dL f f d dL dRTS K L K L ) / ( , = Remembering that and are functions of both K and L and that K will change as L changes along the isoquant (in essence, K is a function of L), we have L f K f dL dK f f L f LK LL L + = and dL dK f f L f KK KL K + = Dr. Steven Waters Econ 380 Page 1 of 7

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L11: Production II therefore, 2 , K KK KL L LK LL K K L f dL dK f f f dL dK f f f dL dRTS + + = Now, we can rearrange this by remembering that Young’s Theorem tells us and we know that along the isoquant KL LK f f = K L f f
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Lecture 11 - Lecture 11 Production II When thou cuttest...

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