Profit Maximization and Comparative Statics
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Today's Agenda
Part 1: Profit Maximization
Part 2: Output Supply & Input Demands
Solving for the optimal quantity
Total profit analysis
Average profit analysis
Marginal profit analysis
Profit-maximizing demands for inputs
Output supply as a function of p
Labor demand as a function of w
Movements along vs. shifts of curves
(optimization)
(comparative statics)
Producer Theory
Exogenous Variables
Endogenous Variables
technology, f()
level of output, y
factors used
total cost, c(y)
Cost Minimization
Production Set
Choice
Rule
factor prices (w, r)
optimal level of output, y*
Profit Maximization
output prices
Total Revenue R(y)
Total Cost, c(y)
Last week
Last time
Today
LONG RUN
SHORT RUN
LONG RUN
SHORT RUN

SHORT RUN


Profit Maximization
Optimize by taking derivative and setting equal to zero:
Profit is total revenue minus total costs:
For a price taker (or competitive firm), revenue equals price times quantity:
LONG RUN
SHORT RUN
Total Profit Analysis


Average Profit Analysis
(multiply by y/y)
(simplify)
(by definition of AR and AC)

Profit may be seen as an area in a unit costs graph.
Note: We can also see total revenues and total costs as areas in a unit cost graph!


Marginal Profit Analysis

Increasing production raises profits
Increasing production lowers profits
Profit as a
Function of Inputs
Total Revenue
Optimize by taking derivatives with respect to each choice variable
and setting equal to zero:
Total Cost
Marginal Revenue Product of each input
Marginal Cost of each input
Conditional vs. Profit-Maximizing Input Demands
Conditional Demands in the Long Run
Profit-Maximizing Demands in the Long Run
Capital and Labor required to produce
a fixed amount of output, y
Capital and Labor required to produce
the profit-maximizing amount of output, y*(w,r,p)
Conditional Demand for Variable Input in the Short Run
Profit-Maximizing Demands for Variable Input in the Short Run
Labor required to produce
a fixed amount of output, y,
given a fixed amount of capital
Labor required to produce
the profit-maximizing amount of output, y*(w,r,p,K),
given a fixed amount of capital
Summary: Profit Maximization
Last Tuesday we established
the relationship between inputs and outputs
via the production function.
Last Thursday we used that production function to
to solve the firm's cost-minimization problem for a specific output \(y\)
and used this to derive its conditional input demands and cost function.
Today we embedded that cost function
into a profit-maximization problem
to determine the optimal output \(y^*\).
The optimal quantity of output also implies profit maximizing levels of inputs.
What happens in the short run run when:
- The price increases
- The wage rate increases
- The rental rate of capital increases
What about the long run?
Econ 50 | Spring 22 | Profit Maximization and Supply
By Chris Makler
Econ 50 | Spring 22 | Profit Maximization and Supply
Profit Maximization and Supply
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