Econ 410: Micro Theory. Recall from last time. Production: Two Variable Inputs. Production: Two Variable Inputs

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1 Slide Slide Econ 0: Micro Theory Production with Multiple Variable Inputs Monday, October 9 th, 007 When both types of inputs become variable, the same amount of output can be produced with different amounts of capital and labor Table 6. in your text Slide Slide Recall from last time We have seen what happens to production when at least one of the inputs is fixed The law of diminishing marginal returns Production is considered in the short run But, what happens to production possibilities in the long run? Both capital and labor inputs become variable Firm can produce output by combining different amounts of labor and capital The information from the table can be represented graphically using isoquants Curves showing all possible combinations of inputs that yield the same output Similarities to indifference curves

2 Slide Slide 7 The isoquant where q = 7 shows all possible combinations of labor and capital that will produce 7 units of output. E A B C D q = Example: units of output can be produced with K & L (point A) OR K & L (point D) q = 7 q = 90 Labor Sprockets is: y K, L KL. Solution: Using the production function, we can create a table of possible output combinations: Output K 00 0 L Slide 6 Slide 8 Sprockets is: y K, L KL. K represents the number of robot hours used in the production process while L represents the number of labor hours. Sketch a representative isoquant for Spacely's production process. Sprockets is: y K, L KL. Solution: We can now plot the points from the table as follows:

3 Slide 9 Slide How can we show diminishing returns to capital or labor with isoquants? Holding one input fixed while varying the other, we can see that output increases at a decreasing rate Example Holding labor constant and increasing capital will lead to diminishing returns from capital in the short and long run. Graphically Substituting Among Inputs Companies must decide what combination of inputs to use to produce a certain quantity of output There is a trade-off between inputs, allowing firms to use more of one input and less of another for the same level of output The slope of the isoquant shows how one input can be substituted for the other while keeping the level of output the same Slide 0 Slide Diminishing Returns A B C Increasing labor holding capital constant (A, B, C) OR Increasing capital holding labor constant (E, D, C) Causes output to increase at a decreasing rate. D q = E q = 7 q = 90 Labor The slope of the isoquant The slope of the isoquant shows how one input can be substituted for the other while keeping the level of output the same The negative of the slope of the isoquant is equal to the marginal rate of technical substitution (MRTS) The MRTS is the amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant

4 Slide Slide Change in Input MRTS Change in Labor Input MRTS K ( for a fixed level of q) L The MRTS and the shape of the isoquant As labor increases to replace capital: Labor becomes relatively less productive becomes relatively more productive Need less capital to keep output constant Isoquant becomes flatter Isoquants and the MRTS We typically assume that the MRTS diminishes along an isoquant. Productivity of any one input is limited Diminishing MRTS occurs because of diminishing returns and implies that isoquants are convex There is a distinct relationship between MRTS and marginal products of inputs. (MP L ) L MRTS ( MP ) K K What is this similar to from consumer theory? Slide Slide 6 / The negative of the slope of the isoquant measures MRTS The MRTS decreases as we move down the indifference curve (substituting labor for capital). / Q =7 Q = Q =90 Labor per month Isoquants: Special Cases Two extreme cases illustrate the possible range of input substitution in production. Perfect substitutes MRTS is constant at all points along a particular isoquant The same amount of output can be produced with: A large amount of capital A large amount of labor A balanced mix

5 Slide 7 Slide 9 Perfect Substitutes Perfect Complements per month A In this case, the same output can be reached with mostly capital or mostly labor (A or C), or with equal amounts of both (B) per month In this case, the same output can only be produced with one set of inputs. B C Q B Q C K Q A Q Q Q Labor per month L Labor per month Slide 8 Slide 0 Isoquants: Special Cases. Perfect Complements This is the case with a fixed proportions production function No substitution is available between inputs Each level of output can be made with only one combination of capital and labor A firm cannot increase output unless both capital and labor are increased in specific proportions For next time We ll continue to look at how firms produce in the long run by discussing economies of scale. Quiz Reminder: Wednesday at the beginning of class Covering sections 6.-6.