4.2. Cost minimization (Producer’s choice optimisation)

The least cost combination of inputs for a given output occurs where the isocost curve is tangent to the isoquant curve for that output.

The slopes of the two curves are equal at that point of tangency.

The firm is operating efficiently when an additional output per dollar spent on labor equals the additional output per dollar spent on machines.So that marginal product per dollar spent should be equal for all inputs:

We define marginal physical product as the additional output that can be produced by employing one more unit of that input while holding other inputs constant:

and

Choosing the Economically Efficient Point of Production can be shown in the graph:

In addition to Lecture 7. Return to scale

Up to the moment we consider a short run, changing one factor while the other is constant. In the long run, all inputs can be increased or decreased simultaneously. The question is how that affect the output and profit. And there are three possible cases in the long run.

Decreasing returns to scale. If an increase in all inputs in the same proportion k leads to an increase of output of a proportion less than k, we have decreasing returns to scale. Example: If we increase the inputs to a dairy farm (cows, land, barns, feed, labor, everything) by 50% and milk output increases by only 40%, we have decreasing returns to scale in dairy farming. This is also known as "diseconomies of scale," since production is less cheap when the scale is larger.

Constant returns to scale. If an increase in all inputs in the same proportion k leads to an increase of output in the same proportion k, we have constant returns to scale. Example: If we increase the number of machinists and machine tools each by 50%, and the number of standard pieces produced increases also by 50%, then we have constant returns in machinery production.

I ncreasing returns to scale. If an increase in all inputs in the same proportion k leads to an increase of output of a proportion greater than k, we have increasing returns to scale. Example: If we increase the inputs to a software engineering firm by 50% output and increases by 60%, we have increasing returns to scale in software engineering. (This might occur because in the larger work force, some programmers can concentrate more on particular kinds of programming, and get better at them). This is also known as "economies of scale," since production is cheaper when the scale is larger.

Lecture 8. Costs and Cost Curves

1. The treatment of costs in Accounting and Economic theory

2. Fixed and variable costs

3. Average costs. Marginal Cost

4. Long run average cost. Returns to Scale

1. The treatment of costs in Accounting and Economic theory

Often decision-makers rely on cost data to choose among production alternatives. In order to use cost data as a "map" or guide to achieve production and/or financial objectives, the data must be interpreted. The ability to make decisions about the allocation and use of physical inputs to produce physical units of output (Q or TP) requires an understanding of the production and cost relationships.

The production relationships and prices of inputs determine costs. Here the production relationships will be used to construct the cost functions. In the decision making process, incomplete cost data is often used to make production decisions. The theory of production and costs provides the road map to the achievement of the objectives.

The price of the factor for the firm is the cost (the amount of money spent to get the factor). To gain better understanding of supply we must to have a closer look for the concept of costs.

Accountants traditionally considered only money costs. Wages, expenditure on raw materials, fuel etc. In this fashion, the net of money revenue minus money cost is called "accounting profit."

Economists understand cost as opportunity cost – the value of the opportunity given up. The most important reasons for using the opportunity cost concept: it helps us to understand the circumstances that will lead people to get into and out of business.

For example, a cab-driver – the self-employed proprietor of an independent cab service – says: "I'm making a 'profit' but is ignoring the opportunity cost of his/her own labor. Let's say that the cab-driver makes $500 a week driving his cab, after all expenses (gasoline, maintenance, etc.) have been taken out. Suppose he can get wages of $800 driving for someone else, with hours no longer and about the same conditions otherwise. Then $800 is the opportunity cost of his labor, and after we deduct the opportunity cost from his $500 net as an independent cabbie, he is actually losing $300 per week. When those opportunity costs are taken into account, we will find that he is not really making a profit after all.

If we have opportunity costs with no corresponding money payments, they are also called implicit costs.

It is interesting to consider the how the opportunity costs, implicit costs look like in different kinds of firms:

– A factory owned by an absentee investor

This is the easiest case to understand. All of the labor costs to the absentee investor are money costs, including the manager's salary. If the investor has borrowed some of the money he invested in the factory, then there are some money costs of the capital invested – interest on the loan. However, we must consider the opportunity cost of invested capital as well. The investor's own money that he has used to buy the factory is money that he/she could have invested in some other business. The return she could have gotten on another investment is the opportunity cost of her own funds invested in the business. This is an implicit cost, and in this case the implicit cost is part of the cost of capital (and probably a fixed cost)

– Family proprietorship or partnership is a store in which family members are self-employed and supply most of the labor. Typically, the owners don't pay themselves a salary – they just take money from the till when they need it, since it is their property anyway. As a result, there are no money costs for their labor. But their labor has an opportunity cost – the salary or wages they could make working similar hours in some other business – and so, in this case, the implicit costs include a large component of variable labor costs.

– A large modern corporation

The corporation has relatively few implicit costs, but generally will have some. All labor costs will be expressed in money terms (though benefits and bonuses have to be included), since the shareholders don't supply labor to the corporation. It will pay interest to bondholders and dividends to shareholders. But the dividends aren't really a cost item – they include profits distributed to the shareholders. Moreover, the typical corporation will retain some profits and invest them within the business, a "plowback" investment. Conversely, shareholders may take a large part of their payout in appreciation of the stock value – and plowback investment is one reason for the appreciation. Thus we would say that the corporation has a net equity value, that is, that the corporation "owns" a certain amount of capital that it invests in its own business (very much like the absentee owner in the first example). This capital has an opportunity cost, and that opportunity cost is an implicit cost. The stockholders, who own the corporation, ultimately receive (as dividends or appreciation) both the opportunity cost of the equity capital and any profit left over after it is taken out.

In economics, all costs are included – whether or not they correspond to money payments. And when we say that businesses maximize profit, it is important to include all costs – whether they are expressed in money terms or not. It is an economics approach to costs. As an economists we included both the implicit costs and money costs in the cost analysis we will make. And economist has Economic profit concept, which means

Accounting profit - implicit costs = economic profit