I. The Profit-Maximizing Firm

University of Pacific-Economics 53

Lecture Notes #7

I.

The Profit-Maximizing Firm

Starting with this chapter we will begin to examine the behavior of the firm. As you may recall

firms purchase (demand) inputs in the factor market and they sell (supply) output in the product

market. We will first look at the production process. The production process is the ability of

the firms to transform inputs into outputs.

All firms face these three basic questions in the production process:

(1) How much output to supply?

(2) How to produce that output? Firms have to decide which technology should be employed

in the production process. Should the firm use a lot of labor and little capital or should

they use a lot of machinery and little labor? We¡¯ll see that the firm chooses the

technology that minimizes the costs for a given level of output.

(3) How much of each input to demand? This answer to this question depends on the

decision made in (2).

A. Profits and Economic Costs

The goal of firms is to maximize profits. Profits (¦Ð) is defined as follows:

Profit = Total Revenue ¨C Total Costs

(¦Ð) =

TR

- TC

Total revenue = Price x Quantity Sold ¡ú TR = P x Q

Total Costs = Explicit Costs

Explicit costs include things such as the cost of labor and the cost of machinery and capital.

Usually when accountants talk about costs they are referring to explicit costs.

Economists on the other hand believe that accounting costs do not fully capture total costs. The

reason is that every input used in the production process has an opportunity cost. This is an

implicit cost. In this class when we refer to profits we will be referring to economic profit.

Economic profit = total revenue ¨C total economic cost

Where total economic cost = explicit cost + implicit cost

Example: Suppose you started your own business and didn¡¯t pay yourself a salary. Accountants

would look at that and say that the cost of labor is $0 since you didn¡¯t pay yourself a wage.

Economists, on the other hand, will say that there is an opportunity cost since you could have

chosen to work for a wage at another firm. Thus the forgone wages are counted as an economic

cost.

B. ormal Rate of Return

How do we define the opportunity cost of capital?

In order to start a business you¡¯ll need to provide start-up capital to get the business going. The

funds are a one-time expenditure that you¡¯ll make at the beginning of your business venture.

The money that one would spend on setting up the business could have been used to open a

savings account, certificate of deposit or to purchase bonds and have earned interest. The lost

interest is the opportunity of capital. This has to be taken into account by individuals when

calculating their true profit.

Example: Suppose you invested $50,000 in your new start-up company, and after one year your

company produces a profit of $2,500. Your rate of return on your initial investment is the

profit divided by the invested amount ($2500/$50.000) = 5%. Is this a good return on your

investment or a bad return on your investment? In order to answer that question we¡¯ll have to

take a look at the opportunity cost of your capital.

Suppose you could have earned 10% interest on a risk-free government bond. If that is the case,

then you ended up earning less return than you could have if you had invested in the bond. The

opportunity cost is the 10% interest you could have returned.

ormal rate of return takes into account this opportunity cost. It is the rate of return sufficient

to keep investors happy. Investors are happy if the rate of return (adjusted for risk) is at least the

same as the interest rate on risk-free government bonds.

We¡¯ll define the normal rate of return = rate of return ¨C opportunity cost of capital

In this case the normal rate of return = 5% - 10% = -5%. If the interest on the bond was 10%,

then you have earned a negative rate of return on your investment. A negative rate of return

does not necessarily mean you are losing money on your investment, it just means you are

earning less return than you could have been.

If the government bond was earning 5%, then you are earning a normal rate of return or zero

economic profits. Note that when we say you are earning 0 economic profit, that is not to say

that your invested earned nothing. It means that your investment earned exactly what you would

have gotten if you invested in a bond.

If the government bond was earning 2%, then you would be earning a normal rate of return of

3% since 5% - 2% = 3%. You are earning a positive rate of return on your investment or

economic profits are positive.

The following example will illustrate the contrast between total costs and total economic costs.

Example: Suppose you are starting up a small business selling belts at a kiosk at the mall. You

estimate that you will be able to sell 3000 belts at $10 each. You will hire one worker and pay

that worker $14,000 a year. You will purchase the belts from a supplier for $5 each.

Additionally, to start your business you will need to purchase a small push cart kiosk that costs

$20,000 (this is your investment in your firm). What is the profit for your firm? What is the

economic profit for your firm?

Let¡¯s calculate the profit.

Total Revenue = P x Q = $10 x 3000 belts = $30,000

Total Costs = Explicit costs

Cost of Labor = $14,000

Cost of Capital = $15,000

Total Explicit Cost = $29,000

Profit = $30,000 - $29,000 = $1,000

However, economists are interested in economic profit not just profit. In order to calculate

economic profit we need to take into account the opportunity cost of capital. The opportunity

cost of capital is the interest the $20,000 in start-up investment could have earned in an

alternative investment. Suppose that alternative investment could have yielded 10% return. The

firm is sacrificing $20,000 x 0.10 = $2,000 in interest. This is the implicit cost of capital. Thus

the new calculation is:

Total Revenue = $30,000

Total Explicit Cost = $29,000

Total Implicit Cost = $2,000

Total Economic Cost = $31,000

Economic Profit = $30,000 - $31,000 = -$1,000

As we shall soon see, if firms earn a positive economic profit, this will be a signal that the

industry is profitable. People will earn a higher return in that industry than they could elsewhere.

You will see new firms entering the industry and existing firms expanding as capital flows to the

profitable industry. Conversely, in the existence of negative economic profits, will cause firms

to contract or leave the industry and capital will flow out.

C. Short-Run vs. Long-Run Decisions

Firms decisions on what to produce, how to produce and how much to produce are affected by

the time frame we are considering. For example, if a firm wanted to expand production, they

simply can¡¯t just build a factory overnight and start producing more output. Economists define

two periods in which the firm responses are different: the short-run and the long-run.

The assumptions we make about the short-run and long-run are illustrated in the following table.

Table 1: Differences between the Short-Run Horizon and Long-Run Horizon

Short-Run

1. A factor of production is fixed

2. No entry or exit possible in the

industry.

Long-Run

1. All factors of production are fully

flexible.

2. Firms are free to enter or leave the

industry.

As seen in Table 1, there are two main differences between short-run and the long-run. In the

short run we assume that at least one factor of production is fixed and the firm cannot change the

that amount of input. Land, labor and/or capital is fixed for firms in the short-run. On the other

hand in the long-run, firms are free to choose any amount of inputs that they wish. Another

difference between the long-run and the short-run is that in the short-run firms cannot enter or

leave the industry. If firms are losing money they can start cutting back operations, but they

cannot shut down. It takes time for firms to properly shut down. In the long-run, firms are free

to come and go from the industry.

II.

The Production Process

We now turn our attention to the production process. Recall that the production process is the

means by which firms are able to turn inputs such as land, labor and capital into final goods and

services. The decision by firms on what production process (technology) to use is important

because it will tell the firm how much inputs will be needed. Much like a household choosing

among goods to maximize utility, firms will choose a combination of inputs that will minimize

costs. There are two broad categories of production process that firms could employ. Firms

could adopt a labor-intensive process which is a technology that relies heavily on labor instead

of machinery. The other option is a capital-intensive process which as the name implies relies

heavily on capital than on labor.

A. The Production Function

A production function is a mathematical equation that shows the relationship between inputs

and outputs. The function tells you given the units of inputs how much output the firm will be

able to produce.

For example, a production function might look like Y = 10KL

Where Y = units of output produced

K = units of capital

L = units of labor

If you have 10 units of capital and 4 units of labor than the firm will be able to produce 400 units

of output.

For the purposes of this class, we¡¯ll make a couple of simplifying assumptions concerning

production functions.

(1) The inputs firms can use are only capital and labor

(2) We¡¯ll assume we are operating in the short-run, and that the amount of capital the firm

has is fixed. The firm can only choose the level of labor.

Table 2 has a sample production function for pizzas

Table 2: Production Function for Pizzas

umber of Workers

0

1

2

3

4

5

Total Pizzas (produced per hour)

0

5

9

12

14

15

Suppose we have a pizza shop set up with a pizza oven, tables and chairs, etc¡­ The capital is

fixed, and the shop owner has to decide how many workers to hire. Obviously, if no workers are

hired then 0 pizzas will be produced. If the shop owner hires one worker, that one worker has to

make the pizza, answer the phones, clean the table and so can only produce 5 pizzas. If the shop

owner hires a 2nd worker, one worker can stay in the kitchen focused on making pizzas, while the

other worker does the other tasks. Thus the total number of pizzas produced is 9 per hour. By

hiring that second worker, the pizza shop¡¯s output of pizza increased by 4 pizzas. This is called

the marginal product of labor (MPL). The marginal product of labor is the additional output

that is produced when one more worker is hired.

Table 3: Marginal Product of Labor

umber of Workers

Total Pizzas (produced per

Marginal Product of

hour)

Labor (MPL)

0

0

N/A

1

5

5

2

9

4

3

12

3

4

14

2

5

15

1

Notice that as the pizza shop hires more workers the added output that each worker brings (the

marginal product of labor) is decreasing. This is due to the fact that the amount of capital is

fixed. Adding more and more workers is not going to result in more and more pizzas being

produced. The reason is that capital is fixed (there is only one kitchen, and one pizza oven) so

adding more workers will not result in pizzas being baked any faster. This decrease in marginal

product of labor is called the law of diminishing returns. The law of diminishing returns states

that adding additional units of one input, while holding another input fixed, will result in output

growing, but at a decreasing rate. In other words the marginal product of that input will be

decreasing.

Figure 1 shows the production function for Table 3 while Figure 2 graphically illustrates the

marginal product of labor.

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