1. Isocosts and isoquants.
Eastwood's ECO 486 Notes
Isocosts and isoquants.
Isocost lines, isoquant curves, and the HO model

2. The behavior of the firm
Eastwood's ECO 486 Notes
The behavior of the firm
Firms are assumed to attempt to maximize profits.
First, the firm must identify the profit maximizing level of output – the quantity where marginal revenue equals marginal cost.
Next, the firm must minimize the cost of producing that level of output.
It must choose the appropriate technology and apply it correctly. As a part of this, it must combine resources according to the least-cost recipe.
Isocost lines, isoquant curves, and the HO model

3. Learning Objectives Calculate and graph a firm’s isocost line
Eastwood's ECO 486 Notes
Learning Objectives
Calculate and graph a firm’s isocost line
Work out how the isocost line changes when resource prices or total cost change
Make a map of production recipes (technology) using isoquants
Explain the choices that firms make
Isocost lines, isoquant curves, and the HO model

4. A Cost Function: Two Resources
Eastwood's ECO 486 Notes
A Cost Function: Two Resources
Assume that there are two resources, Labor (L) and Capital (K).
The money payments to these resources are Wages (W) and Rent (R). An isocost line is similar to the budget line. It’s a set of points with the same cost, C. Let’s plot K on the y axis and L on the x axis.
WL + RK = C; solve for K by first subtracting WL from both sides. RK = C - WL; next divide both sides by R. K = C/R – (W/R)L; note that C/R is the y intercept and W/R is the slope.
Isocost lines, isoquant curves, and the HO model

5. An isocost line K (machines rented) Absolute value of slope equals
Eastwood's ECO 486 Notes
An isocost line
K (machines rented)
Labor hours used in production
Absolute value of slope equals
The relative price of Labor, W/R.
C/R
C/W
Isocost lines, isoquant curves, and the HO model

6. Eastwood's ECO 486 Notes
A Numerical Example
Bundles of: Labor Machine rental
with C = $30 ($6 per labor hour) ($3 per machine hour) a b c d e f
Instructor Notes:
1) The rows of the table list combinations of labor and capital costing $30, rent is $3 per machine hour, and the wage is $6 per hour.
2) For example, row shows us that how much K could be hired for $30: 10 machine hours but no labor.
Points a through f lie on the isocost line for C = $30/hour.
Isocost lines, isoquant curves, and the HO model

7. The Isocost Line a 10 b 8 c 6 d 4 e 2 f 0 1 2 3 4 5 6 7 8 9 10
Eastwood's ECO 486 Notes
The Isocost Line a 10 b
Capital, K (machines rented) 8 c 6 d 4 e 2 f
Labor, L (worker-hours employed)
Isocost lines, isoquant curves, and the HO model

8. The Isocost Line Wage-rental ratio
Eastwood's ECO 486 Notes
The Isocost Line
Wage-rental ratio
With K on the y axis and L on the x axis, the slope of any isocost line equals W/R, the wage-rental ratio. It is also the relative price of labor.
The y-intercept shows the number of units of K that could be rented for $C.
The x-intercept shows the number of units of L that could be hired for $C.
Isocost lines, isoquant curves, and the HO model

9. Changes in One Resource Price
Eastwood's ECO 486 Notes
Changes in One Resource Price
Cost = $30; R = $3/machine
The money wage, W = ... a 10
Capital, K (machines rented) 8 6
A Change
in W 4
…$6 2
…$10 h f
Labor, L (worker-hours employed)
Isocost lines, isoquant curves, and the HO model

10. Changes in Cost 10 A Change 8
Eastwood's ECO 486 Notes
Changes in Cost 10
Capital, K (machines rented)
A Change
in Cost; every point between g and h costs $18. 8 g 6 4
Instructor Notes:
1) Lisa’s income falls from $30 to $15 while the prices of movies and soda remain constant.
2) The budget line shifts leftward, but its slope does not change. 2
W = $6; R = $3;C = $30 h
Labor, L (worker-hours employed)
Isocost lines, isoquant curves, and the HO model

11. Eastwood's ECO 486 Notes
An Isoquant
Each point on a given isoquant represents different recipes for producing the same level of output. 12 10
Capital, K (machines rented) 8 i 6 4
Quantity of Soybeans = 1 (kg./hour) 2 j
Labor, L (worker-hours employed)
Isocost lines, isoquant curves, and the HO model

12. Eastwood's ECO 486 Notes
An Isoquant Map
Different isoquants represents different levels of output. m
Quantity of Soybeans = 2 (kg./hour)
Capital, K (machines rented) k j
Quantity of Soybeans = 1 (kg./hour)
Labor, L (worker-hours employed)
Isocost lines, isoquant curves, and the HO model

13. Eastwood's ECO 486 Notes
Cost Minimization
Choose the recipe where the desired isoquant is tangent to the lowest isocost. 12 a 10
Capital, K (machines rented) 8
C = $36 6 4
W = $6; R = $3;C = $30
equ. 2
C = $18
Labor, L (worker-hours employed)
Isocost lines, isoquant curves, and the HO model

14. Eastwood's ECO 486 Notes
Conclusion: Buy resources such that the last dollar spent on K adds the same amount to output as the last dollar spent on L.
The |slope| of the isocost line = W/R.
The |slope| of the isoquant = MPL/MPK
Isocost lines, isoquant curves, and the HO model