Christopher Makler
Stanford University Department of Economics
Econ 50 : Lecture 15
Labor
Fish
🐟
Capital
Coconuts
🥥
[GOODS]
⏳
⛏
[RESOURCES]
Utility
🤓
The story thus far...
Labor
Fish
🐟
Capital
Coconuts
🥥
[GOODS]
⏳
⛏
[RESOURCES]
🤓
Consumer
The story thus far...
Labor
Firm
🏭
Capital
⏳
⛏
Customers
🤓
This unit: analyze the firms
consumers buy things from
Firm
🏭
Costs
Customers
🤓
This unit: analyze the firms
consumers buy things from
Firm
🏭
Costs
Revenue
From the firm's perspective, they get revenue and pay costs...
Costs
Revenue
Profit
Next week: Solve the optimization problem
finding the profit-maximizing quantity \(q^*\)
...which is what we call profits
Costs
Revenue
Profit
Today: Solve the cost minimization problem
and derive the cost function \(c(q)\)
Costs
Revenue
Profit
Today: Solve the cost minimization problem
and derive the cost function \(c(q)\)
Friday: Derive the revenue function \(r(q)\)
Costs
Revenue
Profit
Today: Solve the cost minimization problem
and derive the cost function \(c(q)\)
Friday: Derive the revenue function \(r(q)\)
Next Monday: Solve the profit maximization problem
Output Supply
Input Demands
Next Wednesday: Analyze the comparative statics
of how the optimal choice changes with prices
for the special case of a price-taking firm
Hicksian Demand
Conditional Demand
pollev.com/chrismakler
If labor is shown on the horizontal axis and capital is shown on the vertical axis, what is the magnitude of the slope of the isocost line, and what are its units?
First Order Conditions
MRTS (slope of isoquant) is equal to the price ratio
Tangency condition: \(MRTS = w/r\)
Constraint: \(q = f(L,K)\)
Conditional demands for labor and capital:
Total cost of producing \(q\) units of output:
A graph connecting the input combinations a firm would use as it expands production: i.e., the solution to the cost minimization problem for various levels of output
Exactly the same as the income offer curve (IOC) in consumer theory.
(And, if the optimum is found via a tangency condition, exactly the same as the tangency condition.)
Conditional demand for labor
Conditional demand for capital
"The total cost of producing \(q\) units in the long run
is the cost of the cost-minimizing combination of inputs
that can produce \(q\) units of output."
Exactly the same as the expenditure function in consumer theory.
If there's only one variable input,
it's perfectly inelastic -- there's only one choice!
Short-run conditional demand for labor
if capital is fixed at \(\overline K\):
Variable cost
"The total cost of producing \(q\) units in the short run is the variable cost of the required amount of the input that can be varied,
plus the fixed cost of the input that is fixed in the short run."
Fixed cost
Short-run conditional demand for labor
if capital is fixed at \(\overline K\):
Total cost of producing \(q\) units of output:
Fixed Costs \((F)\): All economic costs
that don't vary with output.
Variable Costs \((VC(q))\): All economic costs
that vary with output
explicit costs (\(r \overline K\)) plus
implicit costs like opportunity costs
e.g. cost of labor required to produce
\(q\) units of output given \(\overline K\) units of capital
pollev.com/chrismakler
Generally speaking, if capital is fixed in the short run, then higher levels of capital are associated with _______ fixed costs and _______ variable costs for any particular target output.