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Unformatted text preview: C H A P T E R 12 Production with Multiple Inputs This chapter continues the treatment of producer theory when firms are price tak- ers. Chapter 11 focused on the short run model in which capital is held fixed and labor is therefore the only variable input. This allowed us to introduce the ideas of profit maximization and cost minimization within the simplest possible setting. Chapter 12 now focuses on the long run model in which both capital and labor are variable. The introduction of a second input then introduces the possibility that firms will substitute between capital and labor as input prices change. It also intro- duces the idea of returns to scale. And we will see that the 2-step profit maximiza- tion approach that was introduced at the end of Chapter 11 i.e. the approach that begins with costs and then adds revenues to the analysis is much more suited to a graphical treatment than the 1-step profit maximization approach (which would require graphing in 3 dimensions.) Chapter Highlights The main points of the chapter are: 1. Profit maximization in the 2-input (long run) model is conceptually the same as it is for the one-input (short run) model the profit maximizing produc- tion plans (that involve positive levels of output) again satisfying the condi- tion that the marginal revenue products of inputs are equal to the input prices . The marginal product of each input is measured along the vertical slice of the production frontier that holds the other input fixed (as already developed for the marginal product of labor in Chapter 11.) 2. Isoquants are horizontal slices of the production frontier and are, in a techni- cal sense, similar to indifference curves from consumer theory. Their shape indicates the degree of substitutability between capital and labor, and their slope is the (marginal) technical rate of substitution which is equal to the (negative) ratio of the marginal products of the inputs. 231 Production with Multiple Inputs 3. Unlike in consumer theory where the labeling of indifference curves had no cardinal meaning, the labeling on isoquants has a clear cardinal interpreta- tion since production units are objectively measurable. The rate at which this labeling increases tells us whether the production frontiers slope is increas- ing at an increasing or decreasing rate and thus whether the production technology is exhibiting increasing or decreasing returns to scale . 4. Cost minimization in the two-input model is considerably more complex than it was in the single-input model of Chapter 11 because there are now many different ways of producing any given output level without wasting in- puts (i.e. in a technologically efficient way) as indicated by all input bundles on each isoquant. The least cost way of producing any output level then depends on input prices and is graphically seen as the tangency between isocosts and isoquants....
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- Fall '08