Up to this point , we have assumed that the decision as to which resources to use, and in which combinations has already been made by the producer. These decisions are important, however, and require their own, separate investigation. The collection of inputs which a producer chooses in fact defines the process the producer uses. Each separate collection of inputs constitutes a process. Some of the inputs are easily variable, others are not. During the economic Short Run, at least one of the inputs to the process is fixed -- perhaps the plant size, or some difficult to change piece of equipment. During the long run, all inputs are variable. Most economic analysis is confined to the short run, when some input or inputs are fixed. We know that as we add resources to a process in which some input or inputs are fixed, we will eventually encounter diminishing returns. When this occurs, subsequent additions of variable inputs to the process yields smaller and smaller additions to total out put. It is diminishing returns that allows us to talk about maximizing productivity or minimizing costs in the productive process. Were there no diminishing returns, one could produce in infinite amount of output from a given plant.

If all of the inputs to the productive process can be increased, we say we are in a Long Run situation. Under these conditions we can contemplate all possible technologies. As we adopt larger and larger plant sizes, we are increasing what economists call the scale of the operation. If we increase all inputs by a constant factor K { K * (u,v,w,x,y,z)} where u,v,w etc. are inputs and K is a constant (like the number 2 -- so we double all inputs). Assuming we do this, what happens to output Q? Does output Q increase by K*Q, by more than K*Q or by less than K*Q? If output goes up my more than K*Q then we're experiencing economies of scale, and are having increasing returns to scale. If the increase is equal to K*Q, then we've got constant returns to scale. Finally, if we see output go up by less than K*Q, we've got diminishing returns to scale.

As in the analysis of the theory of the firm, we'd like to have a range of increasing returns, then diminishing returns which would suggest a long run economic model that could be subject to optimization (maximization of output and minimization of cost in the long run). The problem, however, arises when one tries to prove diminishing returns to scale. Since you should always be able to get at least constant returns (simply replicate what you already have), why would you ever have diminishing returns. The argument over this question raged for years, leading ultimately to the premise that manageability was what eventually became less efficient. As the firm or firms get larger and larger, it becomes differentially more complex and difficult to manage them. From this, then, we posit diminishing returns to scale, and salvage the ability to optimize under "long run" analysis

The demand for inputs (including labor) depends on how much revenue each unit of input adds to total revenue.

The graph above demonstrates the effect of adding successive units of labor to a tomato patch. At first, labor adds increasing amounts to output, but by the 4 unit of labor, the addition to total output (while positive) has begun to decline. This is the region of diminishing returns. Note that this is a graph of tomato output in bushels. The change in output caused by adding each successive worker is called "marginal physical product" i.e. the amount of physical output added by each additional unit of labor.

The amount we will pay for an input--labor in this case--depends upon the additional revenue generated by that unit. This is not marginal physical product but rather marginal revenue product. Marginal revenue product is simply marginal physical product times the price that the output sells for. In the graph below, we assume that tomatoes sell for $1 per bushel. The dollars of

tomato output equal $1 times the number of bushels produced. If the wage for labor is $5, I will hire labor out to the point where the revenue added by the last unit of labor is equal to $5. That's labor unit number 7. As it happens, all units produce a marginal revenue product in excess of the wage rate. Obviously, unit 8 only produces about $3 worth of MRP, and as such is not worth hiring at $5. The declining portion of the MRP curve is the demand curve for the input, in this case labor. In general, the demand curve for any input equals that input's marginal revenue product MRP curve.

Marginal revenue product depends upon the productivity of the input in the application at hand, and upon the degree to which the product being produced is valued. The higher the price of tomatoes, for example, the higher the MRP of tomato workers. If I come up with a cultivation technique that improves yields, then the MRP of tomato workers is again increased. Note that the demand for tomato labor is derived from the demand for tomatoes. Demands for factors (inputs) are, therefore, derived demands dependent upon the price of the products which the factors produce.

One way to visualize the process of choosing the proper mix of inputs is to look at the choice as one of maximizing output for a given level of expenditure on inputs. If we're choosing between two inputs A and B then the process can look a lot like the indifference curve analysis we've already done.

We have, above, a 3D graph of output and the two inputs. The curved surface is what we call a production function which relates the inputs A and B and the associated level of output. Once again, we want to render this 3D graph in two dimensions. This is done by projecting a "contour map" onto the input A and input B quadrant.

In the graph above, we have projected lines of equal height on the production function to the flat input A, input B quadrant. The object is to get as high on the production function as possible given a budget for inputs (line X--Y). The specific task is to get to the highest isoquant so called because each line is a locus of points of equal (or constant) height on the production function. Iso--meaning constant, quant--designating quantity. Constant quantity. The tangency of the budget line and the highest isoquant is the optimal combination of inputs A and B. Again, this suggests that at the optimal point, the marginal physical product per penny of expenditure for each input will be the same. That is MPPa/Pa = MPPb/Pb. This is the same condition that was called for under utility maximization, except in that case it was marginal utility per penny of expenditure, not marginal physical product.