Efficiency+in+production

Steve Snider
 * Ryan Marks

Efficiency in Production** The main goal with efficiency in production is to determine the correct amount of input needed to produce the estimated amount of output. There are a number of decision criteria that will be looked at to determine the most efficient ways of production. The first is the short-run versus the long-run decisions. The short-term is most commonly referred to as the time where there are fixed costs that exist. For example a capital outlay on a new plant or machine. The long-term on the other hand represents the time frame in which the fixed are compensated for. Let's say the machine is paid over the corse of five years, the long term would be after the five years.

As a manager, it is important to have tools that help to effectivly examine the productivity of the inputs during the production process. In this section we will examine some of the tools that help to measure the productivity of a firm.
 * Measures of Productivity**

The first one of these is Total Product (TP). This looks at the total amount of outputs that can be produced with a given amount of inputs. Lets say that 80 units of input produce 8,000 units of output. This is based on the idea that if all of the inputs are used, than the maximum out put would be the estimated 8,000. An assumption that is used in this is that the labor that is being used will work at maximum capacity. Obviously if the labor was not working at the maximum, we would expect an ouput lower than the maximum of 8,000.

The next one we will look at is the Average Product (AP). This is typically used to find the ouput produced per unit of capital (K) or labor (L). To find the average product of capital (APK), we would devide the output by capital, likewise to find average product of labor (APL), we would devide the output by the amount of labor used. Let's look at an example of how to find the (APL), there is 10,000 units of output and there are 50 units of labor being used. By deviding the output (10,000) by the units of labor used (50) we would end up with an APL of 200.

Another measure is the Marginal Product (MP). The marginal product is used to determine the change in the output that has to do with the last unit of input. In other words, how much benifit did the last unit of input have on production. As with the AP, we will look at both the capital as well as the labor used. However, in this formula we use the change in the output over the change in input. This time we will use an example with the capital as the input, lets say the change in capital input from two to three units (one unit) increases the output by 150 units. Since it would be 150 devided by one, the marginal product of capital (MPK) would be 150.

Lets take a look at these graphically:



Image from: http://content.answers.com/main/content/wp/en/e/e8/Stages_of_production_small.png

First, lets look at which line represents which measurement. The top graph represents the Total Product. This is the first measurement listed, which is a graphical representation of the total output. The second item that was examined was the Average Product. This is represented by the line labled APP. The last item that was examined was the Marginal Product. This can be seen by the line labled MPP. To determine the efficiency, we examine the different stages labeled on the bottom of the chart. The first stage represents increasing marginal returns. Lets use labor for this example. This means that each unit of labor is adding more than one unit of labor at a rate that is increasing (i.e. from one to two labor, output increases 5; from two to three labor, output increases by 10, etc.). The second stage represents the decreasing marginal returns to labor. There is still an increase in output, but the increase is less than the increase for the previous unit (i.e. from 6 to 7 labor, output increases by 5; 7 to 8 labor, output increases 2). The third stage represents the time where the next unit is actually decreasing the total level of output (i.e. labor from 10 to 11, output decreases 5).

The manager of the organization uses this information to determine the best location on the production curve for the organization. No organization should ever exist in the third stage, this is because by adding inputs the outputs are actually decreasing. The optimal point on this production curve above would be B (Y on the lower graph). The reason behind this has to do with the idea that this is where the most output is coming out of one input.

By using formulas, managers are able to determine the correct amount of each of the inputs needed for an organization. In this section we will look at some of the formulas that can be used by managers to determine the best inputs for the firm. As stated previously, capital is represented by K and labor is represented by L. These are used to determine the levels of each needed to produce a specific amount of output.
 * Production Functions**

There are a couple of different functions that are used for production. The one that we will focus on in this section will be Marginal Product for a Linear Production Function. The formula is as follows

Q=f(K,L)=aK + bL

In this equations, a represents the MPk and b represents the MPl. Often this equation is given to determine what the marginal product of labor and capital are. However, this can also be used to figure out what the optimum amount of either Q, L, or K are (assuming that the other items are given). Let's take for example this problem, the goal is 100 units of output wile using 3 units of capital. Given that the firms MPk is 4 and the MPl is 2, through solving we find that the optimum amount of labor is aproximatly 4 (4.16). This formula is often hard to use, the reason for this is because of the amount of givens that are needed to solve. However, it is still usefull in the production aspect.

Let's first look at the idea of Isoquants. These represent the mix of labor and capital that should be used by the firm. In order to better understand this, let's look at a graphical representation. The graph below shows a group of Isoquant curves, labor (L) is on the x axis and capital (K) is on the y axis.
 * Isoquants and Isocosts**



Image taken from: http://210.34.5.27/ews/reading/microeconomics/case/ABcasefair5_06_10.gif

The isoquant curves are convex when viewed graphically. This is because labor and capital are not perfectly substitutable. Moving from the inner curve (most left) to the outer (most right) represents an increase of output. This can be seen by the lable on each of the curves, increasing from 50 to 100, and then to 150. The rate of substitution between the labor and capital is the marginal rate of technical substitution (MRTS). The formula below shows how the MRTS can be determined:


 * MRTS = MPl / MPk**

Isocosts represent combinations of labor as well as capital that will cost the firm the same amount no matter what the combination. The isocost line when used with the isoquant line can show the optimal combination to be used by a firm. The graph below shows Isocost curves along with Isoquant curves:



Image from: http://highered.mcgraw-hill.com/sites/dl/free/0070891540/43154/benjamin_05_03a_300_242.gif

For the Isocost line (straight lines, intersecting both axis'), the x axis is represented by the cost of wage devided by the units of wage rate (cost of labor) and the y axis represnts the cost of capital devided by the rental rate (cost of capital). The total cost can be determined by wL + rK = C. Now lets look at items that would have an affect on the isocost line. Let's say that the firms initial isoquant is the further right (Qa) and the iso cost line is represented by F. This woudl represent a combination where the wage rate outweighs the rental rate. Therefore it is more benificial for the organization to favor capital as an input over labor. The optimal combination is where it touches the isoquant line, which is point A. Now lets say that the wage rate increases (meaning we would want to use less). This would move our point on the wage line toward the origin, and the capital point would remain the same. This woud give us a new isocost line of H (represented with the equation under it). This in turn would affect the isoquant of the organization as well. In order to get the maximum output, the curve would shift from Qa to Qb.

This theory of the Isocost line is one that is important when determining the optimal or most efficient combination of labor and capital. This is something that a manager would be able to use to back up decsisions to either use more labor or more capital. The ultimate goal is to produce the highest amount of outputs with the lowest amount of inputs.

It is important for a firm to produce the highest amount possible with the lowest cost of inputs. This idea of cost minimization can be represented through algebra. The marginal rate of technical substitution MRTS as we stated earlyer is equal MPl / MPk. MRTS also equals the wage rate devided by the rental rate. By substitution we can conclude the following equation to be true:
 * Cost Minimization**


 * MPl/MPk = w/r**

By using this ratio, costs can be reduced for a firm. The end result would be the point in which the isoquant line intersects with the isocost line, which we viewed before. This is useful in the fact that if we are given all or some of the variables we can determine wheather the firm should use more labor or more capital when it comes to the structure of the business.

As we have stated, the goal is to minimize the cost of the inputs to the organization. One way to do this is through the examination of the MRTS. Costs are further examined throughout this site. Total costs including implicit and explicit can be found here: http://mbaecon.wikispaces.com/Total+cost+including+implicit+and+explicit+costs
 * Further Information**

Average cost (long-run and short-run) can be found here: http://mbaecon.wikispaces.com/Average+cost+%28long+run+and+short+run%29

Average variable cost can be found here: http://mbaecon.wikispaces.com/Average+variable+cost

As we can see there are numerous costs that come into play when determining wheather or not to produce or how much of each input to use. One item to note however is that sunk costs are not listed. Sunk cost do not come into play with any of these production decisions, it is sole based on the future prediction.


 * Articles about Production

Improving Efficiency Reduces Production Time** This article discusses how focusing on efficiency in production, the production time for Ford's Michigan Truck Plant has reduced. The way that this was done was through the implimentation of IT solutions, more specifically a wireless network. By usining this new wireless network, the company has been able to increase the output (referring back to our isoquants, this would shift it rightward). The wireless network has been used primarily for tracking, which helps to cut cost. The article states that they were able to avoid $1 million in costs by using the new system. Once again referring back to earlier topics, the company decided to use capital rather than labor. There is no saying that they have not used any labor, but the amount of capital used has outweighed the labor. This article is a good real world example of what companies do to increase the output and reduce the costs in an organization.

Kempfer, Lisa M. "Improving Efficiency Reduces Production Time. (Cover story)." __Material Handling Management__ 61.12 (2006): 44-46. __Business Source Premier__. 5 April 2007. [|http://search.ebscohost.com.] http://web.ebscohost.com/ehost/detail?vid=8&hid=14&sid=18787bfb-f528-4543-8015-296c0de75d88%40sessionmgr7

For the most part, it is easy to understand the idea of efficiency with organizations that have to do with manufacturing. For example, we can see the difference between investing in people or machines. This article takes a look at efficiency in production with a little bit of a different twist. What the company did was reduce the cost per hour (which is the wage rate) to increase the productivity. In contrast to the previous article which used capital, this article uses the labor side of the isocost curves. By reducing the wage rate, the isocost line increases, and shifts the isoquant outward. This reaction has an end result of an increase in production. The article also goes into control systems to make sure that the production amounts are kept up. They have been able to maintain a 100 percent relative efficiency. This article does a good job showing the efficiency of production in a slightly different light.
 * Production Efficiency and the Pricing of Audit Services**

Dopuch, Nicholas, et al. "Production Efficiency and the Pricing of Audit Services." __Contemporary Accounting Research__ 20.1 (2003): 47-77. __Business Source Premier__. 5 April 2007. [|http://search.ebscohost.com.] http://web.ebscohost.com/ehost/detail?vid=13&hid=14&sid=18787bfb-f528-4543-8015-296c0de75d88%40sessionmgr7


 * Example Questions**

1. A reduction in the wage rate will result in... A. Reduction in output B. Increase in output C. No change in output D. Not enough information

2. True or False. The isocost line represents the combination of inputs that will cost the same amount.

3. Diminishing marginal returns can be defined as... A. When the total product (TP) is decreasing. B. When the average product (AP) is decreasing. C. When the range over which marginal product (MP) is positive but declining. D. None of the above.

4. In order to determine the best capital and labor requirements, a manager should use... A. MPL/MPK = W/R B. aK+bL C. Q/L D. All of the above.

5. True of False. A change in the wage rate or rental rate will cause a shift in the isoquant curve.

Answers 1. B, as we know when the wage rate is reduced, we will use more labor and the isoquant curve with shift resulting in more production. Just from this explination we can rule out the other three possible responses, because there is enough information that the production will shift for an increase.

2. True, this is the definition that is given from the textbook.

3. C, the total production has to do with the total quantity. The average product shows how much the average unit of input results in the output. By the process of reason, we can determine the only answer that would result this outcome would effect the marginal product only.

4. A, B shows us the amount of inputs needed to use a specific amount of output. C shows us the average product for labor and not a way of determining the best ratio. Knowing that these answeres are incorrect means we can rule out D. If the manager has this information for the formula, they will be able to determine wheather or not to increase or decrease specific inputs.

5. True, we know from the data given that when the rental rate or the wage rate is changed the isocost curve changes. Since the isocost curve changes, the isoquant curve will change by default.