Chapter 6: Short Run Production And Cost

Dr. Westerhold Econ 330

Handout: Short run production

Production: transforming inputs (land, labor, capital, materials) into outputs (goods and services).

Short Run Production: the time period in which at least one input is fixed (and at least one variable)  Typically assume K (capital) is fixed  Typically assume L (labor) is variable.  The short run will be different for each industry or firm depending on several factors: o Their current production level relative to capacity, o Their financial ability to increase capital, and o Length of long-term contracts.

Production Function: Q=f(K, L, ….)  Q= quantity of output produced  Function of amount of K, L, and other inputs such as materials  A horizontal bar over K indicates the level of capital is fixed (identifies a short run production function)

3 measures of productivity: 1. Total Product (TP): shows the maximum units that can be produced given various levels of K, L.  Total product is the same as “output” or “quantity”, Q.  Measures the total productivity of a production process. o Ex: This quarter Dell computer manufactured a total of 250,000 computers.

2. Marginal Product (MP): measures the change in total product when the level a variable input is changed. For short run production, we will hold constant capital, and vary the level of labor, our variable input.  MP=TP/ L (First derivative of TP function)  As we increase labor by one unit we can see the contribution to total output.  MP is an individual measure of productivity o Ex: If Dell increases its labor force from 100 to 120 workers and production increases from 100,000 to 110,000 units then the marginal product of labor is 10,000/20=500 units. Each additional worker contributes an additional 500 units of product.

3. Average Product (AP): measures the average productivity level of our variable input, labor.  AP= TP/L; also referred to commonly as “labor productivity”  Instead of using an individual measure of productivity we look at the entire labor force or a subset of the labor force and measure its collective productivity.  AP is most commonly used to compare productivity levels across different production sites or across countries.  AP is also used then as a measure of standard of living since productivity and wages are directly linked. Example: Daily Plant Output of Copper Wire Capital Labor TP or Output (in MP (pounds per AP (pounds per person- (Machine (person pounds) person-per hour) per hour) Hours) hours) 40 9 190 40 10 200 40 11 221 40 12 264 40 13 286 40 14 294 40 15 300 40 16 300 40 17 280 A. Fill in the table above B. Graph TP on upper graph (with Labor on the horizontal axis and TP on the vertical axis);Graph MP, AP together on a graph below TP (with labor on the horizontal axis and MP, AP on the vertical axis). Try to line up your labor quantities vertically from the top graph to the bottom graph

GRAPHS Short Run Production Patterns

Initially,  TP increases at increasing rate with increases in labor while MP increases to its maximum point  MP increasing is referred to “Increasing marginal returns to labor”: each additional worker’s contribution exceeds that of the previous worker holding capital constant.  Due to specialization and division of labor.  Occurs between labor units: 0≤ Labor ≤ 11

Then,  TP increases at a decreasing rate with increases in labor and hits its maximum value while MP decreases to zero  MP decreasing is referred to as “Diminishing marginal returns to labor”: each additional worker’s contribution is less than that of the previous worker holding capital constant.  Due to fixed capital.  Occurs between labor units: 11 < labor ≤ 15  Firm MAY hire workers as long as MP >0 so 6 workers in our example. The decision to hire workers depends on each worker’s marginal productivity or contribution to output, the revenue generated from that output, and the cost of production (including labor payments)

Eventually,  TP decreases with additional input of labor, and MP becomes negative  Referred to as “Negative marginal returns” each additional worker hired reduces total product holding capital constant.  Firms never intentionally operate in this segment of the graph.  L > 15  Occurs when overcrowding exists or coordination problems.

Relationship MP and AP:  When MP > AP, then AP increases o When the next worker hired has a contribution to output (MP) greater than the average worker’s contribution the average contribution (AP) will increase.

 When MP < AP then AP decreases o When the next worker hired has a contribution to output (MP) that is lower than the average worker’s contribution the average contribution (AP) will decrease.

 MP=AP at AP max