OUTLINE OF TODAY’S RECITATIONVt = effective value of the firm’s capitalr = weighted average cost of capital of the Firm3.3 Production Costs and optimal production level4.4 Difference between Economies of Scale and Returns to ScaleSloan School of Management 15.010/15.011 Massachusetts Institute of Technology RECITATION NOTES #3 Review of Production and Cost Concepts Thursday - September 23, 2004 OUTLINE OF TODAY’S RECITATION 1. The Production function: brief review of production function and isoquants 2. Economic Cost and User Cost of Capital: definitions 3. Cost concepts: Types of costs and how to calculate them 4. Economies of scale and scope: definition and terminology warnings 5. Learning curve effects: definition and examples 6. Numeric Examples: applying these concepts in practice 1. THE PRODUCTION FUNCTION 1.1 Definition 1.2 Production with one variable input 1.3 Production with two variable input 1.1 Definition In the production process, firms turn inputs, which are also called factors of production, into outputs. We can divide inputs into the broad categories of labor, materials and capital. The relationship between the inputs to the production process and the resulting output is described by a production function. The production function indicates the maximum output Q that a firm will produce for every specified combination of inputs. Assuming for simplicity that there are two inputs, labor L and capital K, the production function can be written as: Q = f(K, L) Example: L measures the number of workers and K the amount of machinery employed by a firm to produce widgets. The production function gives the number Q of widgets that can be produced for any given combination of the inputs. Every production function refers to a given technology. As technology advances, the production function will change to reflect the higher level of output that can be obtained with the same 1inputs. Production functions describe what is technically feasible when the firm operates efficiently. This means that inputs will not be used if they decrease output. The production function also refers to a specific time horizon. In the short run, for instance, some factors of production cannot be changed (e.g. the amount of capital/equipment): these factors are called fixed inputs. Only the variable inputs appear in the production function. In the long run all the inputs are considered variable. 1.2 Production with one variable input Let’s consider the case in which capital is fixed, but labor is variable. In this situation the production function can be written as: Q = f(L) The total product Q will increase by increasing the labor input. At a certain point, however, increasing labor becomes counter productive and the production function reaches its maximum. It does not make sense to add labor above the level that results in the maximum output. The average product of labor is defined as the output per unit of labor input: APL = Q / L Graphically, the slope of the line drawn from the origin to the corresponding point on the total product curve gives the average product of labor (see P&R p.183 for graphs.) In the example, the average product of labor is increasing up to a certain level of labor input, at which point it reaches a maximum, then it starts decreasing. The marginal product of labor is defined as the incremental output per incremental unit of labor input: MPL = ∆Q / ∆L Graphically, the slope of the total product curve at that point gives the marginal product of labor. When the marginal product is greater than the average product, the average product is increasing. This is because the last unit of labor contributes more to output than the previous units, therefore the average goes up. Similarly, when the marginal product is less than the average product, the average product is decreasing. When the APL reaches its maximum, the marginal product of labor must equal the average product of labor, otherwise APL would either be increasing (if MPL > APL) or decreasing (if MPL < APL): MPL = APL when APL is maximum 2When the total product reaches its maximum, MPL = 0 because adding an additional unit of input does not result in any increase in output. The law of diminishing returns holds for most production processes. It states that as the use of an input increases (with other inputs fixed), a point will eventually be reached at which the resulting addition to output decreases. For instance, when labor input is low (and capital is fixed), small increments in labor input add substantially to output as workers are allowed to develop specialized tasks. Eventually, however, it will be more and more difficult to improve output by adding workers while holding the amount of equipment fixed. The extra workers become less effective and the marginal product of labor falls. Diminishing returns refers to changes in quantity of output and not to quality. 1.2 Production with two variable inputs Let’s go back to the general production function with two inputs, labor and capital: Q = F(K, L) This function can be represented graphically using isoquants. An isoquant is a curve that shows all the possible combinations of inputs that yields the same output. (see P&R p. 192 for graphs) The law of diminishing returns still applies. Diminishing returns are observed by holding one variable fixed and looking at the marginal product of the other. Isoquants are typically convex downward sloping curves. Intuitively, this happens because, if output is held constant, it takes less capital to replace one unit of labor when labor is abundant than when it is scarce. The measure of increased output associated with proportional increases in all inputs is fundamental to the long-run nature of the firm’s production process. • If output more than doubles when inputs are doubled, there are increasing returns to scale. This might happen because the increased scale allows more specialization of both workers and equipment. • If output doubles when inputs are doubled, there are constant returns to scale. In other words it is the same to have two identical plants or a bigger plant with twice the labor and the capital. • If output less than doubles when all inputs double, there are decreasing returns to scale. In general, above a certain size,