Production and Costs in the Short Run. Overview. In this section we want to 1) Think about how production might occur and change as different amounts of inputs are used in the production process, and
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In this section we want to
1) Think about how production might occur and change as different amounts of inputs are used in the production process, and
2) Translate the production data into cost data. In other words, we will want to understand how the cost of producing various units of output might change as different amounts of inputs are used.
Inputs can be classified as either fixed or variable.
A variable input is one that can be changed as the level of output is changed .
A fixed input is one that can not be changed as the level of output is changed.
We often think of labor as a variable input and capital or land as a fixed input.
The notion of a fixed or variable input is related to the time frame of production.
The short run is that period of time when at least one input is fixed in amount.
The long run is that period of time in which all inputs are variable.
As an example of this consider fast food in Wayne. About any store in town could remodel and increase floor space in about 3 months. So after 3 months we have the long run, all inputs can vary - even floor space. But less than three months is the short run because there is only so much floor space to use.
In the example, the relationship between the labor used and the total product (TP) is called the short run production function. Behind the scenes we assume there is a given amount of capital.
The marginal product of labor is the additional output forthcoming from the additional unit of labor. Note the first unit of labor has a marginal product of 5.
Note that as the units of labor increases the marginal product first increases, but then begins to diminish after the third unit of labor is employed.
The marginal product curve has the pattern it does because of the way the fixed input is used. Remember that the variable input is used in conjunction with only so much of the fixed input.
In the beginning, as more labor is added, specialization of labor can occur and increasing returns to labor can result, but eventually as more labor is added there will be less of the fixed input to work with and thus additions to output have to diminish.
The way output changes as the variable input is changed, with a given amount of a fixed input, is summarized with the phrase diminishing marginal product.
The average product of labor is for each amount of labor the output produced divided by the labor amount.
The average product mimics, or follows, the marginal product. It is just a math thing.
Next let’s look at some graphs.
In the short run we will consider the fixed and variable costs of production and how they change as more of the variable input is used.
Total cost (TC) = Total variable cost(TVC) + Total fixed cost (TFC).
Marginal cost(MC) = (change in TC)/(change in output). where change in output = 1 when possible.
Average cost (AC) = TC/Q.
Average variable cost(AVC) = TVC/Q.
Average fixed cost(AFC) = TFC/Q.
Note that in the short run fixed costs must be paid whether output is zero or 100,000 units.
Let’s take the production example we had before and translate the production data into cost data. Say the cost of capital is $50 and the cost of labor is $15 per unit.
The next screen shows the continuation of our example.
Note AVC and AC equal MC when AVC and AC are at their minimum values.
When you look back at slide nine at the marginal product and average product curves note that the horizontal axis is measuring labor units used and the curves are inverted u-shaped curves.
When you look back at slide 14 at the marginal cost and various average cost curves note that the horizontal axis is measuring output units and the curves are u-shaped curves.
There is a relationship between these two graphs
The marginal cost of production is the change in total cost divided by the change in output.
The marginal product of labor is the change in output divided by the change in labor.
MC = ▲TC/▲Q, and MPL = ▲Q/▲L, so
MC = ▲TC/(MPL ▲L) = price labor/MPL.