1. What is a production function? How does a long-run production function differ from a short-run production function?
A production function represents how inputs are transformed into outputs by a firm. We focus on the firm with one
output and aggregate all inputs or factors of production into one of several categories, such as labor, capital, and
materials. In the short run, one or more factors of production cannot be changed. As time goes by, the firm has the
opportunity to change the levels of all inputs. In the long-run production function, all inputs are variable.
2. Why is the marginal product of labor likely to increase and then decline in the short run?
When additional units of labor are added to a fixed quantity of capital, we see the marginal product of labor rise, reach a
maximum, and then decline. The marginal product of labor increases because, as the first workers are hired, they may
specialize in those tasks in which they have the greatest ability. Eventually, with the quantity of capital fixed, the
workplace becomes congested and the productivity of additional workers declines.
3. Diminishing returns to a single factor of production and constant returns to scale are not inconsistent. Discuss.
Diminishing returns to a single factor are observable in all production processes at some level of inputs. This fact is so
pervasive that economists have named it the "law of diminishing marginal productivity." By definition, the marginal
product of an input is the additional output generated by employing one more unit of the input, all other inputs held
fixed. The extra output, or returns, to the single input diminish because all other inputs are held fixed. For example,
when holding the level of capital constant, each additional unit of labor has less capital to work with.
Unlike the returns to a single factor, returns to scale are proportional increases in
inputs. While each factor by itself
exhibits diminishing returns, output may more than double, less than double, or exactly double when all the inputs are
doubled. The distinction again is that with returns to scale, all inputs are increased in the same proportion and no input
is held fixed.
4. You are an employer seeking to fill a vacant position on an assembly line. Are you more concerned with the average
product of labor or the marginal product of labor for the last person hired? If you observe that your average product is
just beginning to decline, should you hire any more workers? What does this situation imply about the marginal product
of your last worker hired?
In filling a vacant position, you should be concerned with the marginal product of the last worker hired because the
marginal product measures the effect on output, or total product, of hiring another worker. This in turn will help to
determine the revenue generated by hiring another worker, which can then be compared to the cost of hiring another
The point at which the average product begins to decline is the point where average product is equal to marginal product.