# Lecture 17 - Lecture 17 Input Demand II if ye should serve...

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Input Demand II … if ye should serve him with all your whole souls yet ye would be unprofitable servants. Mosiah 2:21 The Economics Outline 1. Comparative Statics (two inputs) 2. Monopsony 3. Bilateral Monopoly The Mathematics Outline 1. Algebra & Calculus Comparative Statics of Input Demand Two-Input Case Here we continue to be interested in the sign of w L . However, with two (or more) inputs the case gets more complicated. The reason is that with two inputs, we have to consider that as w changes, not only will L change, but the optimal K changes also. With two inputs, we have two optimization conditions, v MP P w MP P K L = = and, as a reminder, ) , ( and ) , ( L K MP MP L K MP MP K K L L = = K L MP and . In other words, as L changes we get a change in both MP , and likewise with any changes in K . As we pursue the two-input case we find that we have to consider two separate effects – the substitution that happens between inputs as the price of one of the inputs changes, and the change in output that happens as the firm finds its profit maximizing quantity to produce. Let’s start with the substitution effect: Substitution Effect: A change in w will change how much labor is demanded and, as a result, how much capital is demanded. Mathematically, a change in w changes the ratio of prices, w/v . This in turn changes the optimal capital/labor ratio. The substitution effect here is how L changes as a result of the change in w . In the following graph, we see that as w falls the substitution effect moves us from point A to point B and the amount of labor demanded unambiguously increases. Dr. Steven Waters

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## Lecture 17 - Lecture 17 Input Demand II if ye should serve...

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