1. ©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.
Short Run Cost Curves
Dr. Jennifer P. Wissink
©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.

2. Jonathan’s New York State Apple Farm
The farm is a business organized to grow and sell apples.
The owner/proprietor, Jonathan, tries to maximize his profits from the business.

3. Jonathan’s Apple Farm Short Run Production Function
The table describes Jonathan’s inputs for the annual production of apples shown in the first column.
Let q=tons of apples, T=acres of land, L=hours of hired labor, M=hours of Proprietor’s time

4. From Production Functions To Seven Short Run Cost Curves
By combining the production function and the factor prices, we produce the firm’s 7 short run cost curves.
Suppose we are given the following information:
Let PL=the price of hired labor per hour.
Let PM=the price of owner’s time per hour.
Let PT=the rental price of land per acre.
Each of the entries in this table represents a price that Jonathan must pay for an input.
Notice that he “pays” for his managerial time because his next best alternative is to earn $12/hour.
He must pay rent for his land.

5. The Seven Short Run Cost Concepts
Total aggregate values
fc = fixed costs = PT•T + PM•M
vc = variable costs = PL•L*(q)
srtc = short run total costs = fc + vc
Average values
afc = average fixed cost = fc/q
sravc = short run average variable cost = vc/q
sratc = short run average total cost = srtc/q = (afc + sravc)
Marginal cost
srmc = short run marginal cost = srtc/q = vc/q

6. Jonathan’s 7 Short Run Cost Curves

7. Graphs Of Jonathan’s Short Run “Totals” Cost Curves
Quantity of apples on the horizontal.
Costs on the vertical.
Fixed Costs are “flat”.
Variable Costs increase with apple production.
They increase at a decreasing rate at first.
They eventually start increasing at an increasing rate.
Short Run Total Costs are simply the vertical sum of fixed and variable costs.

8. Graphs Of Jonathan’s Short Run Marginal & Average Cost Curves
Average Fixed Cost
Average Variable Cost
Short Run Average Total Cost
Short Run Marginal Cost
NOTE: average marginal relation, again.
If the marginal cost is below the average cost, then average cost is falling.
If the marginal cost is above the average cost, then average cost is rising.
Therefore, marginal cost equals average cost when average cost is at a minimum (extreme value).

9. THE GRAPH
1360
485.33
400

10. Short Run Cost Curves With Multiple Variable Factors: Bang/Buck
Suppose there are two types of hired labor: skilled and unskilled, Ls and Lu, with wages per hour Ps and Pu, respectively.
How would this change Jonathan’s cost structure?
Would need to know the short run production function for how skilled and unskilled labor can be substituted for each other.
Suppose we knew this information and that it led to us knowing the marginal product curves for skilled and unskilled labor.
Suppose we are operating where marginal product curves are declining.
How would our derivation of the 7 short run cost curves change?
The only real change occurs in the variable cost function.
vc = Ps•Ls*(q) + Pu•Lu*(q)
How do you determine Ls*(q) and Lu*(q)?
Employ the “equal bang per buck” rule.
So… given the input prices and marginal productivity information, find the combination of skilled and unskilled labor where the following is met:
MPs/Ps = MPu/Pu

11. Example: The Bang/Buck Rule
Suppose q=100 tons of output.
Suppose Ls=10 hours and the MPs at 10 hours is 48 tons.
Suppose Lu=25 hours and the MPu at 25 hours is 30 tons.
Suppose Ps=$24/hour and Pu=$6/hour
Variable cost = $24•10 + $6•25 = $390
Bang/buck in skilled = 48/24 = 2
Bang/buck in unskilled = 30/6 = 5
So… take $1 out of skilled and move it to unskilled labor
You will have the same variable costs.
You will make 3 additional tons of output.
Since you are now using LESS skilled, its marginal product will rise.
Since you are now using MORE unskilled, its marginal product will fall.
The wage rate paid to skilled and unskilled has not changed.
As you substitute unskilled for skilled labor the bang/buck ratios will get closer together.

12. So What?
The 7 short run cost curves will still look and feel and hang together the same way.
We just now know that if there is more than one variable input behind the scenes, the plant manager has successfully carried out the cost minimization exercise correctly and has equated the bang/buck across all variable inputs.
In this way we derive “best” or “minimum” cost functions.

13. What Next?
How do we get long run cost structures?