1. Short Run Costs Lecture 17
Dr. Jennifer P. Wissink
©2017 John M. Abowd and Jennifer P. Wissink, all rights reserved.
March 29, 2017

2. Jonathan’s Apple Farm Cost Structure

3. Jonathan’s Apple Farm Cost Structure

4. Graphs of Jonathan’s Short Run “Totals” Cost Curves
Quantity of apples (q) 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 increase at an increasing rate. WHY?
Short Run Total Costs are simply the vertical sum of fixed and variable costs.

5. 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
THE COST GRAPH

6. THE COST GRAPH
1360
485.33
400

7. Short Run Cost Curves: Locations, Shifts and Movements
Movements Along

8. 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.
NOW... vc = $Ps•Ls*(q) + $Pu•Lu*(q)
So: How do you determine Ls*(q) and Lu*(q)?
Employ the “equal bang per buck” rule.
So… given the input prices and marginal productivity information, find the combination of skilled and unskilled labor where the following is met:
at LS*(q) and LU*(q) you need to have [MPs/$Ps] = [MPu/$Pu]

9. Example: The Bang/Buck Rule
Suppose q=100 tons of apples.
Suppose: Ls=10 hours & the MPs at 10th hour is 48 tons.
Suppose: Lu=25 hours & the MPu at 25th hour is 36 tons.
Suppose Ps=$12/hour and Pu=$6/hour
Jonathan’s Variable Cost = $12•10 + $6•25 = $270
Bang/buck in skilled = MPs/$Ps = 48/$12 = 4 tons
Bang/buck in unskilled = MPu/$Pu = 36/$6 = 6 tons
i>clicker Question Given this information, to make q=100 tons of apples more cost efficiently, Jonathan should A. do nothing – he’s doing great! B. use more Skilled and the same Unskilled. C. use only Skilled. D. use more Skilled and less Unskilled. E. use more Unskilled and less Skilled.
tons 48
mpskilled 10
Hours Skilled Labor
tons 36
mpunskilled 25
Hours Unskilled Labor

10. Example: The Bang/Buck Rule
RECALL:
Bang/buck in skilled = MPs/Ps = 48/12 = 4
Bang/buck in unskilled = MPu/Pu = 36/6 = 6
So… hire 1 less skilled worker, and with the money saved, hired as many unskilled workers as you can. What happens?
Variable costs will stay the same.
You’ll hire 1 less skilled worker and 2 more unskilled workers (based on the two wages).
You will produce 48 fewer tons using 1 less skilled worker, but…
You will produce 72 more tons using 2 more unskilled workers, so….
For the same costs, you now have produced 24 more tons of apples!
NOW WHAT WILL THE “Bang/buck” ratios look like?
tons 48
mpskilled 10
Hours Skilled Labor
tons 36
mpunskilled 25
Hours Unskilled Labor

11. 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 his variable inputs.
In this way we derive the “best” or “minimum” cost functions.
THE COST GRAPH

12. Now What?

13. Short Run Profit Maximization, Finally…
Profit () = total revenue (tr) – short run total cost (srtc).
(minimum or best) short run total cost
Profit depends on the firm’s output level (q).
That is:  (q) = tr(q) - srtc(q).
Firm’s problem:
choose q* to maximize  where  (q) = tr(q) - srtc(q).
Note:
Marginal revenue (mr) = tr/q
Marginal cost (srmc) = tc/q

14. Rules For Profit() Maximization in the Short Run
If q* maximizes (q) = tr(q) – srtc(q) , then
(1) mr(q*) = srmc(q*)
the first order condition, or f.o.c.
(2)  (q*) is a maximum and not a minimum
the second order condition, or s.o.c
(3) at q* it is worth operating:  (q*>0)   (q=0)
NOTE: This procedure is good, no matter what type of firm considered.

15. Intuition: Why mr=mc at the Profit Maximizing q*
Why? Because....
If mr > mc at q, then…
If mr < mc at q, then…
If mr = mc at q, then…