I. The Profit-Maximizing Firm

Transcription

1 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 (π) is defined as follows: Profit = Total Revenue Total Costs (π) = TR - TC Total revenue = Price x Quantity Sold 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 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.

2 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 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

3 $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 Long-Run 1. A factor of production is fixed 1. All factors of production are fully flexible. 2. No entry or exit possible in the 2. Firms are free to enter or leave the industry. industry.

4 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

5 Table 2: Production Function for Pizzas umber of Workers Total Pizzas (produced per hour) 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 2 nd 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 hour) 0 0 N/A Marginal Product of Labor (MPL) 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.

6 Output (Number of Pizzas per hour) Figure 1 Production Function Number of Workers Marginal Product of Labor (Number of Pizzas per Hour) Figure 2 Marginal Product of Labor Number of Workers B. Average Product of Labor A related concept to marginal product of labor is the average product of labor (APL). The average product of labor is simply the total amount produced divided by the number of workers. Average Product of Labor (APL) = Total Output Produced/(Total Number of Workers) Table 4: Average Product of Labor umber of Workers Total Pizzas (produced per hour) Marginal Product of Labor (MPL) 0 0 N/A N/A Average Product of Labor (APL)

7 You should be clear between the distinction between average product and marginal product. The average product will always follow the marginal product. That is if the marginal product is below the average product, the average will fall. Conversely, if the marginal product is above the average product the average will increase. Figure 5: Average Product of Labor Figure 5 shows the 6 average product of labor for our pizza 5 example. The average product of labor is the red 4 curve. The blue curve is the 3 marginal product of labor. Notice that 2 since the marginal product of labor is below the average 1 product of labor throughout, this 0 causes the average to fall. Output Number of Workers A simple example will illustrate why the average always follows the marginal but doesn t change as quickly. In baseball, there is a statistic called batting average which indicates the average number of times a player has hit a base hit. For example a batting average of means that 25% of the time the player had reached base on a hit. What if a player had a batting average and then had a great night and had 4 hits all 4 times he came to bat. His batting average for the night was 100%. This is his marginal product. How will it affect his average? It should cause it to increase (but not all the way to 1.00). Similarly, if the player had a bad night and went hitless (0 for 4), then we would expect his average to fall, but again it won t fall all the way down to 0. In general: If the marginal is greater than the average, the average will rise. If the marginal is lower than the average, the average will fall. This is an important concept that will be used extensively in the chapters that follow. Be sure you understand the relationship between the marginal and average. III. Choice of Technology How do firms decide what technology to employ? Should they use a lot of labor or should they use a lot of capital to produce a given amount. A key consideration that firms take into account is the cost of inputs. If labor is very expensive relative to capital, we would expect firms to

8 choose a technology that is more capital intensive (that is a production process that relies heavily on capital). On the other hand if labor is cheap and capital expensive then we would expect the opposite to occur. Consider a firm that produces 150 widgets and has to choose among three technologies.. The choice facing the firm is illustrated in Table 5. Technology Units of Capital Units of Labor A 3 10 B 4 7 C 5 5 The firm has three choices in to produce 150 widgets. The can choose to use 3 units of capital and 10 units of labor to get to 150 widgets. They could also use 5 units of capital and 5 units of labor to produce the same amount. Technology A is more labor intensive, Technology B is slightly less labor intensive, while Technology C uses a balance of capital and labor. How does the firm decide? Suppose the firm is facing the following input prices. The price of capital =$100 per unit of capital The price of labor = $80 per worker Calculate the total cost of the different technologies Technology A = (3 x $100) + (10 x $80) = $1100 Technology B = (4 x $100) + (7 x $80) = $960 Technology C = (5 x $100) + (5 x $80) = $900 Technology C is the cheapest option. The firm is able to produce its 150 widgets cheapest using Technology C. What if the firm was in a low wage country? Suppose that the price of capital is still $100 but wages are $40. How will this affect the choice of technology by the firm? Calculate the total cost of the different technologies Technology A = (3 x $100) + (10 x $40) = $700 Technology B = (4 x $100) + (7 x $40) = $680 Technology C = (5 x $100) + (5 x $40) = $700 Now with the cheaper wages, Technology B is the cheapest option. Note that technology B uses more of the cheap input than Technology C. When the price of labor falls, the firm will substitute away from capital and towards labor. Key Point: Profit-maximizing firms will choose the technology that minimizes the cost of production.