How to Calculate an Isocost Line
An isocost line is every input bundle with the same total cost: wL + rK = C. Its intercepts are C ÷ w and C ÷ r, and its slope is −w ÷ r.
The Isocost Line formula
Calculator
Enter the cost budget, the wage and the rental rate to get both intercepts, the slope and the cost of one bundle.
The spending level this particular isocost line is drawn for.
Price of one unit of labor.
Price of one unit of capital.
Workers in the input combination you are checking against the line.
Machines in the same input combination.
Spending the whole budget on workers hires 30, which is where the line meets the labor axis.
- Most capital the budget buys
- 60
- Capital given up per extra worker
- 2
- Cost of this input bundle
- $1,200
- Budget left over
- $0
- Where the bundle sits
- On the isocost line
Spending it all on machines rents 60, the other end of the same line.
The slope is that figure with a minus in front, so one more worker costs 2 machines at constant total cost.
Each input priced out and added together comes to $1,200.
After paying for the bundle the firm still holds $0 of the budget.
Bundles on the line spend the budget exactly, bundles inside it leave money unspent, and bundles outside it cost more than the firm has.
How to calculate Isocost Line, step by step
- 1Write the isocost equation. wL + rK = C covers every combination of labor and capital that costs the firm exactly C, where w is the wage and r is the rental rate.
- 2Find the labor intercept. C ÷ w is the most labor the budget buys, the point where the line meets the horizontal axis because capital is zero.
- 3Find the capital intercept. C ÷ r is the most capital the budget buys, the point where the line meets the vertical axis.
- 4Compute the slope. Slope = −w ÷ r, the units of capital that have to be given up to afford one more unit of labor without changing total cost.
- 5Test a bundle against the line. Multiply each input by its price and add. A bundle costing exactly C sits on the line, a cheaper one sits inside it, and a dearer one is out of reach.
Worked example: Isocost Line
A firm has $1,200 to spend, labor costs $40 per worker and capital rents for $20 per machine. Spending it all on labor buys 1,200 ÷ 40 = 30 workers, and spending it all on capital rents 1,200 ÷ 20 = 60 machines, so those two points are the intercepts. The slope is −40 ÷ 20 = −2, meaning one more worker costs 2 machines. The bundle of 20 workers and 20 machines costs (20 × $40) + (20 × $20) = $800 + $400 = $1,200, so it sits exactly on the isocost line with nothing left over.
Isocost Line questions
What happens to the isocost line when the wage rises?
It pivots inward on the labor axis. C ÷ w falls while C ÷ r stays put, so the line gets steeper and the firm substitutes toward capital to hold cost down.
How is an isocost line different from a budget constraint?
Same algebra, different actor. A budget constraint sets a consumer's spending on two goods against income, while an isocost line sets a firm's spending on two inputs against a total cost figure.
Where on the isocost line does the firm produce?
At the bundle where the line just touches the isoquant for the output it wants. That tangency is the point where MRTS equals w ÷ r, which is the least-cost way to make that output.
What shifts the whole isocost line outward?
A larger cost budget with input prices unchanged. Both intercepts grow in the same proportion, so the new line is parallel to the old one.
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated