1. Managerial Economics & Business Strategy
Chapter 5
The Production Process and Costs

2. How do we know the OPTIMAL level of capital and labor in the long run
Isoquant
The combinations of inputs (K, L) that yield the producer the same level of output.
Shape reflects how managers can substitute inputs and maintaining the same level of output.

3. Isoquants are Convex  K and L are not perfect substitutes
Capital
Increase Output
Q2= 300 units
Q1= 200 units
Q0= 100 units
Labor
Substitute Labor for Capital

4. Marginal Rate of Technical Substitution (MRTS)
Slope of the Isoquant
How much of the “other” variable do you need to keep output constant?
The rate at which two inputs are substituted while maintaining the same output level.

5. Linear Isoquants Capital and labor are perfect substitutes Q = aK + bL
MRTSKL = b/a
Substituted at a constant rate, independent of the input levels employed. Q3 Q2 Q1
Increasing Output L K

6. Leontief Isoquants Capital and labor are perfect complements.K
Increasing Output
Capital and labor are perfect complements.
Capital and labor are used in fixed-proportions.
Q = min {bK, cL}
No input substitution along isoquants
So…. no MRTSKL L

7. Cobb-Douglas Isoquants
Inputs are not perfectly substitutable.
Diminishing marginal rate of technical substitution.
As less of one input is used in the production process, increasingly more of the other input must be employed to produce the same output level.
Q = KaLb
MRTSKL = MPL/MPK K Q3
Increasing Output Q2 Q1 L

8. Isocost
The combinations of inputs that produce a given level of output at the same cost:
wL + rK = C
Rearranging,
K= (1/r)C - (w/r)L
For given input prices, isocosts farther from the origin are associated with higher costs.
Slope is the ratio of input prices
Price of labor / price of capital
Changes in input prices change the slope of the isocost line. K
New Isocost Line associated with higher costs (C0 < C1).
C1/r C0
C0/w
C0/r C1 L
C1/w K
New Isocost Line for a decrease in the wage (price of labor: w0 > w1).
C/r
C/w1 L
C/w0

9. Cost Minimization Slope of the isoquant and isocost are equal
What was the slope of the isoquant?
Marginal Rate of Technical Substitution
What was the slope of the isocost?
Price ratio
Marginal product per dollar spent should be equal for all inputs:
But, this is just

10. Slope of Isocost = Slope of Isoquant
Cost Minimization K
Point of Cost Minimization Q L
Slope of Isocost = Slope of Isoquant

11. Optimal Input Substitution
If we start at point A at a cost of C0.
Suppose w0 falls to w1.
The isocost curve rotates counterclockwise
Cannot use original level of capital like we did with consumption.
Need to keep output constant
Substitute Labor for capital because it’s cheaper
Now can produce at point B using more labor and less capital to produce the same output K A K0
C1/w1 B K1 L1 Q0 L0
C0/w0 L

12. Cost Analysis Types of Costs Fixed costs (FC) Variable costs (VC)
Total costs (TC)
Sunk costs