Review of Basic Microeconomic Relations

Lecture Outline

• Economic Optimization
  • Optimal Decisions
  • Maximizing the Value of the Firm
• Basic Economic Relations
  • Functional Relations: Equations
  • Totals, Averages, and Marginals, and their Functional Relationships
• Marginal Analysis and Profit Maximization
• Incremental Analysis (Managerial Econ Application)

I. Economic Optimization

In microtheory and its application area, managerial economics, we assume that the units of analysis, and their objectives, can be characterized as follows:

• Firms: Profit maximizers
• Individuals (consumers, managers, workers, etc): Utility (satisfaction) maximizers
• Government: Maximizing over the weighted utilities of the controlling interest groups

First consider firms as profit maximizers. More specifically, firms are assumed to have as an objective the maximization of the expected present value of the firm for its owners (e.g., shareholders), also known as expected present value maximization:

(Expected Profit, year 1)/(1+i)^1 + (Expected Profit, year 2)/(1+i)^2 + ... + (Expected Profit, year n)/(1+i)^n

where 'i' is the rate at which the firm discounts a payoff in the future relative to a payoff today (why do firms and people discount future payoffs? What rates are typical discount rates today in the US?). The '^' symbol means raising the parenthetic term preceding the symbol to the power that follows the symbol (e.g., 'X^2' refers to the value X² ). Expected profit refers to the situation in which revenues and costs are at least somewhat uncertain in the future, and the term 'expected' usually means a type of weighted averaging of all possible states of nature or possible outcomes for the variable in question.

For example, if expected profits each year over a 20-year planning horizon are $100,000, and if the firm discounts the future at the rate of 10%, then the expected present value of the firm is $851,356.

What are some of the contraints on expected present value maximization?

Expected present value analysis for an entire firm is complex and thus costly for the firm to conduct with great frequency, and so is usually confined to major planning decisions (expansion, new capitialization, product line change, merger/acquisition, technological change, etc). This type of optimization analysis is also referred to as global optimization or strategic optimization.

Much more common within firms, particularly at operating unit levels, is partial or tactical optimization analysis, which takes as given the broad constraints, requirements, and goals of prior global optimization, and represents the day-to-day tactics that are consistent with the global plan.

The optimization decision-making process involves two steps:

• Important economic relations need be expressed in analytic terms (e.g., parameters and parameter values).
• Optimization techniques need be applied so that parameter values that best suit the firm's (management's) objectives

Formal economic optimization techniques yield quality outcomes that are directly proportional to the quality of the inputs. What I mean by quality of inputs is whether or not the analyst has fully parameterized all the relevant factors affecting the managerial decision. Insight and intuition are valuable managerial qualities, and may not be amenable to parameterization, meaning that formal analytical outcomes must be combined with insight and intuition in order to make the 'best' managerial decision.

Management in modern corporations works for shareholders. Thus we say that managers are agents of the shareholders. Shareholders wish to maximize the expected present value of the firm. Managers may or may not have the same incentives. For example, what are the incentives of a manager receiving a fixed salary and limited promotion opportunities? Are they different from those of the shareholders? How might shareholders align the incentives of managers with maximizing the expected present value of the firm? If corporate raiders seek out poorly managed companies for takeovers, then how might this competitive "market for corporate control" create discipline and align the incentives of agents?

What is profit? What is the difference between business or accounting profit on the one hand, and economic profit on the other? Which one is normally reported in the business news?

What is the normal rate of return? It is the minimum profit necessary to attract and retain investment.

What is profit margin? It is profit divided by sales revenue.

What is return on shareholders' equity? It is business or accounting profit divided by the book value of the firm. What is the book value of the firm? It is the value of the firm's assets, measured at cost, rather than the earnings capacity (the economic or market value) of those assets.

Why might firms receive profit in excess of the normal rate of return?

1. Frictional profit theory: Unanticipated changes in an industry cannot be adjusted to instantaneously
2. Monopoly
3. Innovation
4. Efficiency

What are the roles that profit performs in the economy?

Basic Economic Relations

We can then plot these data as follows in figure 2.a:

Relationships between totals, averages, and marginals:

Note that the average of something is total/units, and marginal is the change in totals. For example:

1. average profit is: (total profit)/(total output)
2. marginal profit is: [(total profit, output=x)-(total profit, output=(x-i))]/i

From the example in the table given above, we can plot total, average, and marginal profits in Figure 2.b below:

The "y" variable on a diagram such as the one above is the dependent variable, while the "x" variable is the independent variable.

Marginal Analysis and Profit Maximization

profit = (P-B)Q - CQ² - A,

then using optmization calculus we can find the Q where profit hits its peak (see figure 2.b above) by taking the partial derivative of profit with respect to Q, and setting that partial derivative equal to zero. By setting that partial derivative equal to zero we are finding the spot where, a small change in Q has no effect on profit (the peak). This point occurs where marginal revenue equals marginal cost.

• Marginal revenue = (change in total revenue)/(1 unit change in Q)
• Marginal cost = (change in total cost)/(1 unit change in Q)

If we change (increase) Q by 1, total cost goes up by B units plus 2CQ units, which can be found by taking the partial derivative of TC with respect to Q:

1. TC = A + BQ + CQ²
2. MC = B + 2CQ.

Profits are maximized when MR = MC. If we increase Q beyond that point, then MR is less than MC, and so costs go up by more than revenues go up on that unit sold. If we decrease Q, then MR is greater than MC, and we can usually increase profit by increasing Q. Thus profit cannot be increased when:

MR = MC

Which means that P = B + 2CQ. Solving for Q gives us:

Q = (P-B)/2C. Since P = $100, and B = $20, and C = $1, then we have

Q = $90/$2 = 45 units.

Thus marginal profit is positive when Q is between 0 and 45, and falls below 0 for Q greater than 45.

The breakeven point occurs when total profit = 0.

NOTE: A tangent line indicates the slope of a curve at the point of tangency. If we were to draw a tangent line at the peak of the total profit curve above, what would it's slope be? What is the economic interpretation?

Incremental Analysis

The Hirschey/Pappas text has a nice example of incremental analysis on pages 47-48. I would like the students to construct a similar, but different, incremental analysis problem.