Inputs and Costs Inputs and Costs a. Production function
September 21, 2006 How inputs and outputs are related Diminishing returns Reading: Chapter 8 b.Cost function and cost curve Total cost Begin examination of how firms make decisions using the How cost function is related to production principles of individual decision making (marginal costs and function benefits) First we examine relation between inputs and outputs c. Marginal and average cost Second we examine costs and marginal (and other) costs d.Short-run and long-run costs and returns to scale Next topic: Marginal benefits for the firm and how they decide how much to produce 2
Production Function Production Function Definitions Total product curve Production function: relationship between the quantity of inputs a firm uses and the quantity of output it The total product curve shows how the quantity of output produces. depends on the quantity of one variable input, for a given quantity of other inputs. Inputs are of two types: Fixed input: an input whose quantity is fixed and cannot Assume: be varied in the relevant time preriod. firm produces one product Variable input: an input whose quantity the firm can vary in the relevant time period. with two inputs, labor and land amount of land held constant So labor is variable input and land is fixed input Time periods: Short run: time period in which at least one input is fixed. Long run: time period in which all inputs can be varied. Why? Some things take longer to change than others
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Production Function Production Function Total product curve, cont. Marginal Product
The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input. The marginal product of labor is the additional quantity of output produced by using one more unit of labor.
We have diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that Diminishing returns input. Marginal product can be negative – total product falls as input 5 increased. 6
1 Production Function Production Function Marginal Product of Labor Curve Shifts in total and marginal product curves The total and marginal product curves for labor shift when: 1. Amount of other (fixed) factor changes 2. Technology changes
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Cost Cost Definitions Total Cost Curve
Fixed cost: cost that does not depend on the quantity of output produced. It is the cost of fixed inputs. In our example, it is the cost of land Variable cost: cost that depends on the quantity of output produced. It is the cost of variable inputs for any level of output. In our example, it is the cost of labor Total cost: Fixed cost + Variable cost TC = FC + VC The relation between output and costs is called the total cost function and shown with a total cost curve. The total cost curve shows how total cost depends on output. 9 Slope increases due to diminishing returns to labor 10
Cost Marginal and Average Cost From total product curve to total cost curve Marginal Cost output labor
Total product curve
labor output
Cost = labor x wage Cost
Total cost
Variable cost Variable cost
output Fixed cost output 11 12
2 Marginal and Average Cost Marginal and Average Cost Average Total Cost Curve Average Cost
Average total cost, often referred to simply as average cost, is total cost divided by quantity of output produced: ATC = TC/Q Average fixed cost is the fixed cost per unit of output: AFC = FC/Q Average variable cost is the variable cost per unit of output: The average total cost curve is U-shaped. At low levels of output, average total AVC = VC/Q cost falls because the “spreading effect” of falling average fixed cost dominates the “diminishing returns effect” of rising average variable cost. 13 At higher levels of output, the opposite is true and average total cost rises.14
Marginal and Average Cost Marginal and Average Cost Average cost and marginal cost curves Relation between marginal and average cost
¾ At the minimum-average cost output, average cost is equal to marginal cost. ¾ At output less than the minimum- average cost output, marginal cost is less than average cost and average cost is falling. ¾ And at output greater than the minimum- average cost output, marginal cost is greater than average cost and average cost is rising. ¾ Holds for both average total and average variable cost. Why?
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Marginal and Average Cost More Realistic Cost Curves Short-Run and Long-Run Costs In the short-run, fixed cost is given and outside the control of a firm.
Marginal and Average Variable costs can be downward sloping, at least In the long-run the quantity of all inputs is at some levels of output. variable: “fixed” cost may also be varied. In the long run a firm’s “fixed cost” becomes a variable it can choose. For instance, plant Marginal cost curves do not always slope upward. The benefits of size, or size of farm, can be changed. specialization of labor can lead to increasing returns at first represented by a downward-sloping marginal cost curve. Once there are enough workers to permit specialization, however, diminishing returns set in. 17 18
3 SR and LR Costs Short-run and Long-run Costs Long-Run Average Total Cost Curve Changes in fixed costs Long-run average total cost curve shows relationship There is a trade-off between output and between higher average total cost when fixed cost and lower variable cost fixed cost has been for any given chosen to minimize output level, and average total cost for vice versa. each level of output, by choosing the But as output goes up, average total appropriate amount of cost is lower with the fixed factor(s) the higher amount of fixed cost. Not the minimum point of each SR ATC, but lower envelope 19 20
Short-Run and Long-Run Average Short-run and Long-Run Costs Total Cost Curves Economies and Diseconomies of Scale ¾ There are economies of scale when long-run average total cost declines as output increases. ¾ Specialization (division of labor) at higher levels of output ¾ There are diseconomies of scale when long- run average total cost increases as output increases. ¾ Problems of coordination and communication ¾ There are constant returns to scale when long-run average total cost is constant as output increases. ¾ Replication 21 ¾ Replication 22
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