Managerial Economics Eighth Edition Truett + Truett Chapter 5: Production Analysis John Wiley & Sons, Inc. 9/18/2018 Slides by Jim Witsmeer

Chapter 5 Outline Theory of Production Long Run Production Production Function Least Cost Production Substitution of Inputs Economic Region & Expansion Path Returns to Scale Short Run Production Law of Diminishing Returns Profit Maximization 9/18/2018

Corporations and Production Hollow Corporations Virtual Corporations Production Technology Production efficiency in the: Long run all inputs can vary Short run some inputs are fixed 9/18/2018

Production Function Where; Q is output quantity L is labor input K is capital input E is energy input C is catalyst input We will focus on the two primary input variables labor and capital 9/18/2018

Least-Cost Production What is least-cost production and how is it measured and achieved? Least Cost Production occurs when the inputs are combined in such a way that the cost is minimum. Marginal Product tells how much output we get from an additional unit of input. Greater marginal product means lower cost per additional unit of output. NOTE: Unit cost of output varies inversely with input productivity. or 9/18/2018

Production Function Plot 9/18/2018

Isoquants An isoquant is a contour, which contains all input combinations yielding the same production output 9/18/2018

Marginal Rate of Substitution Marginal Rate of Substitution (MRS) is the rate at which one input can be substituted for another without changing the production output. The MRS is related to the slope of the isoquant at any combination of inputs INCREASED QUANTITY ΔK ΔL The MRS is the negative of the slope of the isoquant 9/18/2018

MRS related to Marginal Product If we move along an isoquant (Q is constant) then the impact of increasing one input must be offset by the decrease in the other input. therefore: Or The rate at which one input can be substituted for another is inversely related to their productivities 9/18/2018

Substitution of Inputs Three categories of substitution Not substitutes Perfect substitutes Imperfect substitutes See Figure 5-6 of the text We have been looking at imperfect substitutes where the MRS varies depending on your operating point. 9/18/2018

Least-Cost Combination of Inputs The MRS is the Marginal Rate of (Technical) Substitution because it is substitution while maintaining constant output. For every production output quantity there is a unique combination of inputs that minimizes cost called the Least-Cost Combination of Inputs. 9/18/2018

Isocost Lines An isocost line is a line containing all input combinations that result in the same cost. The cost equation is: PK = $1/unit K PL = $2/unit L INCREASED COST Cost = $6 With constant cost: 9/18/2018

Test for Least-Cost Combination The tangent point between an isocost and an isoquant represents least cost. With constant cost: Increase cost until the curves first touch this is the least-cost combination  With constant quantity:  Therefore at the least–cost combination: 9/18/2018

Economic Region of Production Ridge lines are lines which connect all the points where MPK and MPL are zero. The region between the ridge lines is called the economic region of production In the long run, a profit oriented firm will never employ input combinations outside the ridge lines. 9/18/2018

Expansion Path Given the slope of the isocost line (input price ratio), each isoquant has a unique least-cost combination point. A least-cost point occurs whenever an isocost line is tangent to an isoquant. These points can be connected to form an expansion path. In the long run, the firm will expand by moving out the path that connects these points. 9/18/2018

Returns to Scale If output changes are more proportional to a given proportion of change in all inputs, there are increasing returns to scale. If output changes are less proportional to a given proportion of change in all inputs, there are decreasing returns to scale. If output changes are exactly proportional to a given proportion of change in all inputs, there are constant returns to scale. 9/18/2018

Short Run Production Optimization In the long run all inputs are variable while in the short run only a limited number of inputs can be varied due to time and capital constraints. However the same least-cost approach that we developed for the long run can be used to compare alternative production strategies in the short run. In our study of the short run, we will assume K is fixed and only L is variable. 9/18/2018

Short Run Definitions TOTAL PRODUCT / unit time (with only L variable) AVERAGE PRODUCT MARGINAL PRODUCT or 9/18/2018

Law of Diminishing Returns The law of diminishing marginal productivity states in the short run productivity will fall as output is increased. MPL = 0 A line from the origin is tangent to Total Product curve at the maximum average product. APL = MPL APL is maximum Three significant points are: MPL is maximum 9/18/2018

Cost Savings in the Short Run The combination L0 and K0 are least cost. In the short run K is fixed at K0. Any input L other than L0 will result in other than least cost. K If the input required is I1 then input L can be reduced to point E. KO KO If the utilization of K is flexible a better option is to operate at point G even though reduction in L, using only part of the K0 units of K and saving on use of L. L LO 9/18/2018

Profit Maximization The objective is not to minimize cost but to maximize profit: Not the same thing. We will show that for variable L profit is maximum when: Where: MRPL is the Marginal Revenue Product of input L. NMR is the Net Marginal Revenue obtained from each additional unit of production output, Q. MCL is the Marginal Cost of input L. 9/18/2018

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