Handout #7
Production and Cost
Production function
Production function is the relationship between quantity of inputs used to make a
good and the quantity of output of that good.
Marginal product
Marginal production is the increase in outpout that arises from an additonal unit
of input. Usually, the marginal product is increasing for a particular amount of output. If
a producer keeps increasing the production, eventually, the marginal product is
diminishing as quantity of the input incresases. The explanation is that variable factors
such as workers have to share equipment (fixed factors) and work in more crowded
conditions. As more workers are hired, additional workers contributes less to the
production process.
Given that Y is quantiy of output and QL is quantity of workers.
Y
MPL 
QL
Cost curve
From the production function, we can find the total cost. Suppose we use two
factors, namely labor (L) and capital (K) in the production process, total cost (TC) is:
TC  PL QL  PK QK
Where PL is a wage rate for employing one unit of labor
PK is a rental rate for employing one unit of capital
Measures of costs
1. Fixed vs variable costs
Fixed costs are costs that do not vary with quantity of output produced. In the
above example, fixed cost is the cost of hiring capital, which is PK QK .
Varaible costs are costs that do vary with quantity of output produced. Therefore,
variable cost in the above example is PLQL .
2. Average vs Marginal cost
Total cos t (TC )
Average total cost (ATC) =
Y
Total cos t (TC )
Marginal cost =
= slope of the total cost curve
Y
Totalfixed cos t (TFC )
Average fixed cost (AFC) =
Y
Total var iable cos t (TVC )
Average variable cost (AVC) =
Y
Example 1: A firm has fixed costs of $20,000. It can hire workers for $2,000. Complete
the following table about the firm’s cost structure:
NUMBER
OF
WORKERS
TOTAL
OUTPUT
0
0
1
100
2
300
3
700
TOTAL
FIXED
COST
TOTAL
VARIABLE
COST
TOTAL
COST
AVGE
FIXED
COST
AVGE
VARIABLE
COST
AVGE
TOTAL
COST
MARGINAL
COST
Shapes of cost curves
- Marginal cost first is decreasing when quantity of output produced increases. Marginal
cost is eventually rising as the quantity of output increases.
- The average total cost and average variable cost curves are U-shaped
- The marginal cost curve crosses the average total cost and average variable cost curve at
their minimum point.
- Whenever marginal cost is less than average total (variable) cost , averagt total (variable)
cost is falling. Whenever, marginal cost is greather than average total (variable) cost,
average total cost is rising.
The relationship between marginal cost and marginal product
Whenever marginal product increases, marginal cost is decreasing. Whenever
marginal product decreases, marginal cost is increasing.
Costs in the long run
In the long run, all factors are variable.
- Constant returns to scale: Long-run average total cost stays the same as the quantity
output changes.
- Increasing returns to scale (economies of scale) : Long-run average total cost falls as the
quantity of output increases.
- Decreasing returns to scale (diseconomies of scale) : Long-run average total cost rises
as the quantity of output increases.