Worksheet for Unit 6 – Production and Cost Curves
Welcome to Jim’s Farm (apologies to anyone who actually knows anything about real farming – but this is just an econ example, the numbers are unrealistic). Based on many years of records, Jim expects that how much wheat he produces depends upon how many workers he hires. It’s a really simple farm, with only two inputs to the production process: acres of land and workers. When Jim combines the quantity of land listed in column a with the number of workers in column b, the farm can produce the output listed in c. | ||||||||||
Assumptions: Land rents for $500 per acre for the entire season. Workers get paid $100 each per season (they are only used at harvest time).
Suggestion: You may want to download the following data table here as a .csv file and open it with Excel or other spreadsheet. |
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Inputs | Output | |||||||||
a. | b. | c. | d. | e | f | g | h | i | j | k |
Acres of Land | Workers | Bushels of Wheat (Total Product) | Marginal Product | Total Fixed Cost | Total Variable Cost | Total Cost | Marginal Cost | Avg Fixed Cost (AFC) | Avg Variable Cost (AVC) | Avg. Total Cost (ATC) |
30 | 0 | 0 | ||||||||
30 | 1 | 50 | ||||||||
30 | 2 | 125 | ||||||||
30 | 3 | 225 | ||||||||
30 | 4 | 315 | ||||||||
30 | 5 | 385 | ||||||||
30 | 6 | 445 | ||||||||
30 | 7 | 490 | ||||||||
30 | 8 | 520 | ||||||||
30 | 9 | 540 | ||||||||
30 | 10 | 550 |
INSTRUCTIONS: You should either print this table out and complete it by hand, or you may wish to copy the first three columns into a spreadsheet to make calculations easier. You need to complete columns d through k using the information provided in the first three columns and in the description and assumptions above.
TIP 1: The definition of “marginal product” is the “increase in total physical output when one more unit of input (in this case labor) is added.
TIP 2: The definition of “marginal cost” is the “increase in total cost when one more unit of product is produced”. When you get to column h you will notice that the data on Total Product doesn’t increase one unit at a time. For example, Total Product increases from 0 units to 50 units in going from the first line to the second line of data. To really calculate the exact “Marginal Cost” for the 50th unit of output we SHOULD have data on Total Cost for 49 units and Total Cost for 50 units. We don’t have the Total Cost for 49 units. So, we need to estimate the Marginal Cost. To to this, calculate how much the Total Cost column increases from line to the next line, then divide that increase by the Marginal Product (how much output increased in that same step increase). That should give you a reasonable estimate of Marginal Cost.
Questions (you enter your answers in the Learning Management System for your school):
- How much additional output (bushels of wheat) will be produced by adding the third worker?
- What was the marginal product of the seventh worker?
- Which worker is the first worker to be hired that results in diminishing marginal returns?
- What is the Total Fixed Cost when six workers are being used?
- What are the Total Costs to produce 490 bushels using 7 workers?
- If farmer Jim desired to produce wheat at the lowest average total cost for each bushel, how many workers should he hire?
- How many workers would be hired and used, if farmer Jim desires to produce at the lowest possible average variable cost?
- What level of output (bushels of wheat) results in the lowest average fixed cost?
- Compare the Marginal Product column to the Marginal Cost column. Which statement below is most correct? Statements (order of statements may change in learning mgt system):
- both MP and MC keep increasing
- both MP and MC keep decreasing
- MP reaches its highest at 3 workers and then begins to decline. MC reaches it lowest at 3 workers and then begins to rise. This not a coincidence. It must always happen this way since greater productivity means making more with less, which lowers the cost of production.
- If Jim’s objective is to maximize total profits, how many workers should he hire?