23 - The Citadel



23. Short Run Production in Excel

Questions:

1. Build an excel spreadsheet showing the production function, the short run production function, the short run cost function, the marginal product and marginal product of labor function.

Production in the Spreadsheet

Put the long run production function in the spreadsheet. Put the numbers and symbols in separate cells. Put the capital, wage rate, and rental rate of capital below.

Then put the short run production function on the spreasheet. Use the amount of capital on the spreadsheet and the long run function to calculate the short run function.

Use the short run production function to find the amount of labor needed to produce a given amount of output. (Solve L in terms of Q.)

Use the wage rate on the spreadsheet and the amount of labor to find variable cost as a function of Quantity—the variable cost function.

Use the given amount of capital and rental rate on capital to find the fixed cost function.

Put the fixed and variable cost functions together to find the total cost function.

Use the short run production function to find the marginal product function.

Put the marginal revenue function for the revenue and demand sheet onto the short run production sheet.

Marginal Product of Labor Schedule

A marginal product of labor schedule relates the amount of labor used to its marginal product. The first column would be units of labor. Use a formula that allows the increment by which labor increases and the intitial level of labor to be adjusted.

The second column should be the amount of output that amount of labor can produce. This is found by the short run production function. Don’t forget to anchor. And then, the third column would be the marginal product of labor from the marginal product of labor function.

Marginal Revenue Product of Labor Schedule

The marginal revenue product of labor schedule is easy to build. Add a column with the marginal revenue. This requires the marginal revenue function, but using the column of outputs that go with each amount of labor, (the short run production function) marginal revenue is easy to find. Then add a column with the marginal revenue product of labor. It is just equal to the marginal product of labor multiplied by the marginal revenue.

The result looks something like:

|L |Q |MPl |MR |MRPl |

|0 |0 | | | |

|1 |50 |50 |10 |500 |

|2 |90 |40 |8 |320 |

|3 |120 |30 |5 |150 |

|4 |140 |20 |3 |60 |

|5 |150 |10 |2 |20 |

|6 |155 |5 |1.5 |7.5 |

|7 |158 |3 |1 |3 |

Graphing

A graph of labor and the marginal revenue product of labor is the demand for labor curve. It gives the most a firm would be willing to pay and still hire a given amount of labor. Alternatively, it gives the amount of labor a firm will buy at a given wage—or more exactly, the amount of labor a firm should hire to make the most profit. Don’t forget that to skip columns that you don’t need, you hold down the control button.

Because the marginal product is undefined with an output of zero, start graphs at one (or at least something other than zero.)

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