Skip to main content

Exercise: Table of Production

You are given the following table of production, fill in the blank. Then graph the total product, average product and marginal product curves with respect to labor.
Labor (L)  Capital (k)  Output (Q)  Average Product (Q/L)   Marginal Product
4 3 51 ... n.a
5 3 ... 12.4 ...
6 3 ... ... 7
7 3 ... ... 2
8 3 ... 8.75 ...

The solution is:
Labor (L)  Capital (k)  Output (Q)  Average Product (Q/L)   Marginal Product
4 3 51 (51/4) n.a
5 3 62 (62/5) 11
6 3 69 (69/6) 7
7 3 71 (71/7) 2
8 3 70 (70/8) -1

If you know the average output and the number of workers (labor) then you know the output at each level (recall the formula for AP). If you know the marginal product for a given number of workers, and if you know the previous total output for one less worker then you can find the total output for the given number of workers:



Let's graph the total product curve as a function of labor input:
Just by looking at this graph, one can observe that the slope (the rate of growth) of the total product curve is becoming smaller and smaller as the number of workers increases.

 Let's graph the APL (average product of labor) and MPL (marginal product of labor) curves as functions of labor input:

We can see that since the APL curve is decreasing, the MPL (marginal product of labor) must be below. Furthermore, as the number of workers increases from 4 to 7, the production experiences diminishing returns, the production increases at a decreasing rate as new workers are added. Finally when a 8th worker is added to the production line, we see that the firm is facing decreasing returns, the firm produces less than it would have without the additional worker. 


One easy way to find the marginal product of x (where x can be labor, capital, etc..) is by simply taking the partial derivative of a production function with respect to x. In other words:



The production function is represented by f(x,y,k) this means that the production function f depends on three different inputs or variables, namely x, y, and k (but it can depend on more or less variables). We take the derivative with respect to x, so we treat the other variables as constant. This gives us a general formula for the MP of x for this specific production function. Then, all we need to do is to plug into the derivative the different values of x,y,k (if possible, the derivative could just be a constant). 
Labels:

Comments

Post a Comment

Popular posts from this blog

Macroeconomics: real vs nominal gross domestic product

Nominal GDP:   A nominal GDP measures the value of a nation's output produced in a year, given the prices charged for that year. However, if prices increase while the output level stays constant in a given year, the nominal GDP will drastically increase, even though the level of production is equal to that of the previous year. Estimating real GDP: To determine the actual change in output from one year to the next, we must adjust the nominal value of a country's output in a year based on changes in the average price level during that year.  Inflation is when the price level increases, whereas deflation is when the price level is decreasing. To determine whether the nominal GDP overestimates or underestimates the output of a country, one must know whether the average price level has increased or decreased. In order to achieve this task can use a price index known as the GDP deflator. The GDP deflator: Real GDP is calculated by replacing the prices for that current year with tho...
Post a Comment
Read more

Microeconomics: Firms and cost in the short run

In Economics, the term short run refers to a time period where at least one variable of interest does not change . In our case, the short run for a firm is when at least one input  (labor, land, capital) stays fixed. Usually land and capital are considered fixed in the short run.  If an input is fixed during a period time, no matter how much the total product a firm produces, its cost stays the same. This cost is commonly known as fixed cost (FC). Examples of fixed costs: rent, property taxes, loan payments. Labor is often considered to be a part of the  variable cost (VC) . Variable cost can be defined as the cost a firm has control over during the short run. Unlike fixed cost, variable cost increases (decreases) as a firm's total product increases (decreases). Examples of variable costs include: utility bills, wages, raw materials A firm's total cost (TC) is the sum of its variable and fixed costs. As you can see, the fixed cost...
Post a Comment
Read more

Macroeconomics: aggregate supply in the short run

Aggregate supply -short run analysis- : The aggregate supply is the total amount of goods and services the firms in a country produce at each price level in a fixed period of time. Sticky-wage and price model: In the short run, wages and other costs of production are relatively fixed. In other words, workers will not accept to receive a lower wage, when firms want to reduce their costs. Thus, firms must reduce output and layoff workers when aggregate demand drops. However, firms can also benefit from these fixed costs, if the aggregate demand increases (i.e shifts to the right). Prices increases but the costs stay the same, firms earn a bigger profit in the short run. Short run aggregate supply curve (SRAS): The SRAS curve is upward sloping, but is relatively flat below the full-employment level of output because of the "stickiness" of wages. The SRAS curve is relatively steep beyond the full employment level of output, since the firms are  physically constraint to ...
Post a Comment
Read more