1.3 — Perfect Competition I

ECON 326 • Industrial Organization • Spring 2023

Ryan Safner
Associate Professor of Economics
safner@hood.edu
ryansafner/ioS23
ioS23.classes.ryansafner.com

Outline

Short Run Production Concepts

Costs in the Short Run

Costs in the Long Run

Revenues

Recall: The Firm's Two Problems

1^st Stage: firm's profit maximization problem:

Choose: < output >
In order to maximize: < profits >

2^nd Stage: firm's cost minimization problem:

Choose: < inputs >
In order to minimize: < cost >
Subject to: < producing the optimal output >

Minimizing costs $⟺$ maximizing profits

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$
Graph: find $q^{*}$ to max $π ⟹ q^{*}$ where max distance between $R (q)$ and $C (q)$

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$
Graph: find $q^{*}$ to max $π ⟹ q^{*}$ where max distance between $R (q)$ and $C (q)$
Slopes must be equal: $M R (q) = M C (q)$

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$
Graph: find $q^{*}$ to max $π ⟹ q^{*}$ where max distance between $R (q)$ and $C (q)$
Slopes must be equal: $M R (q) = M C (q)$

At $q^{*} = 5$ :
- $R (q) = 50$
- $C (q) = 40$
- $π (q) = 10$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

At low output $q < q^{*}$ , can increase $π$ by producing more: $M R (q) > M C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

At high output $q > q^{*}$ , can increase $π$ by producing less: $M R (q) < M C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

$π$ is maximized where $M R (q) = M C (q)$

Comparative Statics

If Market Price Changes I

Suppose the market price increases
Firm (always setting MR=MC) will respond by producing more

If Market Price Changes II

Suppose the market price decreases
Firm (always setting MR=MC) will respond by producing less

The Firm’s Supply Curve

The firm’s marginal cost curve is its supply curve^‡ $p = M C (q)$
- How it will supply the optimal amount of output in response to the market price
- Firm always sets its price equal to its marginal cost

^‡ Mostly...there is an important exception we will see shortly!

Calculating Profit

Calculating (Average) Profit as AR(q)-AC(q)

Profit is $π (q) = R (q) - C (q)$

Calculating (Average) Profit as AR(q)-AC(q)

Profit is $π (q) = R (q) - C (q)$
Profit per unit can be calculated as: $\begin{aligned} \frac{π (q)}{q} & = A R (q) - A C (q) \\ = p - A C (q) \end{aligned}$

Calculating (Average) Profit as AR(q)-AC(q)

Profit is $π (q) = R (q) - C (q)$
Profit per unit can be calculated as: $\begin{aligned} \frac{π (q)}{q} & = A R (q) - A C (q) \\ = p - A C (q) \end{aligned}$
Multiply by $q$ to get total profit: $π (q) = q [p - A C (q)]$

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $10
At q* = 5 (per unit):
At q* = 5 (totals):

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $10
At q* = 5 (per unit):
- AR(5) = $10/unit
At q* = 5 (totals):
- R(5) = $50

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $10
At q* = 5 (per unit):
- AR(5) = $10/unit
- AC(5) = $7/unit
At q* = 5 (totals):
- R(5) = $50
- C(5) = $35

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $10
At q* = 5 (per unit):
- AR(5) = $10/unit
- AC(5) = $7/unit
- A $π$ (5) = $3/unit
At q* = 5 (totals):
- R(5) = $50
- C(5) = $35
- $π$ = $15

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $2
At q* = 1 (per unit):
At q* = 1 (totals):

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $2
At q* = 1 (per unit):
- AR(1) = $2/unit
At q* = 1 (totals):
- R(1) = $2

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $2
At q* = 1 (per unit):
- AR(1) = $2/unit
- AC(1) = $10/unit
At q* = 1 (totals):
- R(1) = $2
- C(1) = $10

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $2
At q* = 1 (per unit):
- AR(1) = $2/unit
- AC(1) = $10/unit
- A $π$ (1) = -$8/unit
At q* = 1 (totals):
- R(1) = $2
- C(1) = $10
- $π$ (1) = -$8

Short-Run Shut-Down Decisions

What if a firm's profits at $q^{*}$ are negative (i.e. it earns losses)?
Should it produce at all?

Short-Run Shut-Down Decisions

Suppose firm chooses to produce nothing $(q = 0)$ :
If it has fixed costs $(f > 0)$ , its profits are:

$\begin{aligned} π (q) & = p q - C (q) \end{aligned}$

Short-Run Shut-Down Decisions

Suppose firm chooses to produce nothing $(q = 0)$ :
If it has fixed costs $(f > 0)$ , its profits are:

$\begin{aligned} π (q) & = p q - C (q) \\ π (q) & = p q - f - V C (q) \end{aligned}$

Short-Run Shut-Down Decisions

Suppose firm chooses to produce nothing $(q = 0)$ :
If it has fixed costs $(f > 0)$ , its profits are:

$\begin{aligned} π (q) & = p q - C (q) \\ π (q) & = p q - f - V C (q) \\ π (0) & = - f \end{aligned}$

i.e. it (still) pays its fixed costs

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \\ p q - V C (q) - f & < - f \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \\ p q - V C (q) - f & < - f \\ p q - V C (q) & < 0 \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \\ p q - V C (q) - f & < - f \\ p q - V C (q) & < 0 \\ p q & < V C (q) \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \\ p q - V C (q) - f & < - f \\ p q - V C (q) & < 0 \\ p q & < V C (q) \\ p & < A V C (q) \end{aligned}$

Shut down price: firm will shut down production in the short run when $p < A V C (q)$

The Firm’s Short Run Supply Decision

The Firm's Short Run Supply Decision

Firm’s short run supply curve:

{\begin{cases} p = M C (q) & if p \geq A V C \\ q = 0 & If p < A V C \end{cases}

The Firm's Short Run Supply Decision

Firm’s short run supply curve:

{\begin{cases} p = M C (q) & if p \geq A V C \\ q = 0 & If p < A V C \end{cases}

Summary:

1. Choose $q^{*}$ such that $M R (q) = M C (q)$

Summary:

1. Choose $q^{*}$ such that $M R (q) = M C (q)$

2. Profit $π = q [p - A C (q)]$

Summary:

1. Choose $q^{*}$ such that $M R (q) = M C (q)$

2. Profit $π = q [p - A C (q)]$

3. Shut down if $p < A V C (q)$

Summary:

1. Choose $q^{*}$ such that $M R (q) = M C (q)$

2. Profit $π = q [p - A C (q)]$

3. Shut down if $p < A V C (q)$

Firm's short run (inverse) supply:

${\begin{cases} p = M C (q) & if p \geq A V C \\ q = 0 & If p < A V C \end{cases}$

1.3 — Perfect Competition I

ECON 326 • Industrial Organization • Spring 2023

Ryan Safner
Associate Professor of Economics
safner@hood.edu
ryansafner/ioS23
ioS23.classes.ryansafner.com

Outline

Short Run Production Concepts

Costs in the Short Run

Costs in the Long Run

Revenues

Recall: The Firm's Two Problems

1^st Stage: firm's profit maximization problem:

Choose: < output >
In order to maximize: < profits >

2^nd Stage: firm's cost minimization problem:

Choose: < inputs >
In order to minimize: < cost >
Subject to: < producing the optimal output >

Minimizing costs $⟺$ maximizing profits

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$
Graph: find $q^{*}$ to max $π ⟹ q^{*}$ where max distance between $R (q)$ and $C (q)$

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$
Graph: find $q^{*}$ to max $π ⟹ q^{*}$ where max distance between $R (q)$ and $C (q)$
Slopes must be equal: $M R (q) = M C (q)$

Visualizing Total Profit As $R (q) - C (q)$

$π (q) = R (q) - C (q)$
Graph: find $q^{*}$ to max $π ⟹ q^{*}$ where max distance between $R (q)$ and $C (q)$
Slopes must be equal: $M R (q) = M C (q)$

At $q^{*} = 5$ :
- $R (q) = 50$
- $C (q) = 40$
- $π (q) = 10$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

At low output $q < q^{*}$ , can increase $π$ by producing more: $M R (q) > M C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

At high output $q > q^{*}$ , can increase $π$ by producing less: $M R (q) < M C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

$π$ is maximized where $M R (q) = M C (q)$

Comparative Statics

If Market Price Changes I

Suppose the market price increases
Firm (always setting MR=MC) will respond by producing more

If Market Price Changes II

Suppose the market price decreases
Firm (always setting MR=MC) will respond by producing less

The Firm’s Supply Curve

The firm’s marginal cost curve is its supply curve^‡ $p = M C (q)$
- How it will supply the optimal amount of output in response to the market price
- Firm always sets its price equal to its marginal cost

^‡ Mostly...there is an important exception we will see shortly!

Calculating Profit

Calculating (Average) Profit as AR(q)-AC(q)

Profit is $π (q) = R (q) - C (q)$

Calculating (Average) Profit as AR(q)-AC(q)

Profit is $π (q) = R (q) - C (q)$
Profit per unit can be calculated as: $\begin{aligned} \frac{π (q)}{q} & = A R (q) - A C (q) \\ = p - A C (q) \end{aligned}$

Calculating (Average) Profit as AR(q)-AC(q)

Profit is $π (q) = R (q) - C (q)$
Profit per unit can be calculated as: $\begin{aligned} \frac{π (q)}{q} & = A R (q) - A C (q) \\ = p - A C (q) \end{aligned}$
Multiply by $q$ to get total profit: $π (q) = q [p - A C (q)]$

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $10
At q* = 5 (per unit):
At q* = 5 (totals):

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $10
At q* = 5 (per unit):
- AR(5) = $10/unit
At q* = 5 (totals):
- R(5) = $50

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $10
At q* = 5 (per unit):
- AR(5) = $10/unit
- AC(5) = $7/unit
At q* = 5 (totals):
- R(5) = $50
- C(5) = $35

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $10
At q* = 5 (per unit):
- AR(5) = $10/unit
- AC(5) = $7/unit
- A $π$ (5) = $3/unit
At q* = 5 (totals):
- R(5) = $50
- C(5) = $35
- $π$ = $15

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $2
At q* = 1 (per unit):
At q* = 1 (totals):

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $2
At q* = 1 (per unit):
- AR(1) = $2/unit
At q* = 1 (totals):
- R(1) = $2

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $2
At q* = 1 (per unit):
- AR(1) = $2/unit
- AC(1) = $10/unit
At q* = 1 (totals):
- R(1) = $2
- C(1) = $10

Calculating (Average) Profit as AR(q)-AC(q)

At market price of p* = $2
At q* = 1 (per unit):
- AR(1) = $2/unit
- AC(1) = $10/unit
- A $π$ (1) = -$8/unit
At q* = 1 (totals):
- R(1) = $2
- C(1) = $10
- $π$ (1) = -$8

Short-Run Shut-Down Decisions

What if a firm's profits at $q^{*}$ are negative (i.e. it earns losses)?
Should it produce at all?

Short-Run Shut-Down Decisions

Suppose firm chooses to produce nothing $(q = 0)$ :
If it has fixed costs $(f > 0)$ , its profits are:

$\begin{aligned} π (q) & = p q - C (q) \end{aligned}$

Short-Run Shut-Down Decisions

Suppose firm chooses to produce nothing $(q = 0)$ :
If it has fixed costs $(f > 0)$ , its profits are:

$\begin{aligned} π (q) & = p q - C (q) \\ π (q) & = p q - f - V C (q) \end{aligned}$

Short-Run Shut-Down Decisions

Suppose firm chooses to produce nothing $(q = 0)$ :
If it has fixed costs $(f > 0)$ , its profits are:

$\begin{aligned} π (q) & = p q - C (q) \\ π (q) & = p q - f - V C (q) \\ π (0) & = - f \end{aligned}$

i.e. it (still) pays its fixed costs

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \\ p q - V C (q) - f & < - f \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \\ p q - V C (q) - f & < - f \\ p q - V C (q) & < 0 \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \\ p q - V C (q) - f & < - f \\ p q - V C (q) & < 0 \\ p q & < V C (q) \end{aligned}$

Short-Run Shut-Down Decisions

A firm should choose to produce no output $(q = 0)$ only when:

$\begin{aligned} π from producing & < π from not producing \\ π (q) & < - f \\ p q - V C (q) - f & < - f \\ p q - V C (q) & < 0 \\ p q & < V C (q) \\ p & < A V C (q) \end{aligned}$

Shut down price: firm will shut down production in the short run when $p < A V C (q)$

The Firm’s Short Run Supply Decision

The Firm's Short Run Supply Decision

Firm’s short run supply curve:

{\begin{cases} p = M C (q) & if p \geq A V C \\ q = 0 & If p < A V C \end{cases}

The Firm's Short Run Supply Decision

Firm’s short run supply curve:

{\begin{cases} p = M C (q) & if p \geq A V C \\ q = 0 & If p < A V C \end{cases}

Summary:

1. Choose $q^{*}$ such that $M R (q) = M C (q)$

Summary:

1. Choose $q^{*}$ such that $M R (q) = M C (q)$

2. Profit $π = q [p - A C (q)]$

Summary:

1. Choose $q^{*}$ such that $M R (q) = M C (q)$

2. Profit $π = q [p - A C (q)]$

3. Shut down if $p < A V C (q)$

Summary:

1. Choose $q^{*}$ such that $M R (q) = M C (q)$

2. Profit $π = q [p - A C (q)]$

3. Shut down if $p < A V C (q)$

Firm's short run (inverse) supply:

${\begin{cases} p = M C (q) & if p \geq A V C \\ q = 0 & If p < A V C \end{cases}$

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1.3 — Perfect Competition I

ECON 326 • Industrial Organization • Spring 2023

Ryan Safner Associate Professor of Economics safner@hood.edu ryansafner/ioS23 ioS23.classes.ryansafner.com

Outline

Recall: The Firm's Two Problems

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Profit Per Unit As MR(q)MR(q) and MC(q)MC(q)

Visualizing Profit Per Unit As MR(q)MR(q) and MC(q)MC(q)

Visualizing Profit Per Unit As MR(q)MR(q) and MC(q)MC(q)

Comparative Statics

If Market Price Changes I

If Market Price Changes II

The Firm’s Supply Curve

Calculating Profit

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

Short-Run Shut-Down Decisions

The Firm’s Short Run Supply Decision

The Firm’s Short Run Supply Decision

The Firm's Short Run Supply Decision

The Firm's Short Run Supply Decision

The Firm's Short Run Supply Decision

The Firm's Short Run Supply Decision

The Firm's Short Run Supply Decision

The Firm's Short Run Supply Decision

Summary:

Summary:

Summary:

Summary:

Outline

Help

1.3 — Perfect Competition I

1.3 — Perfect Competition I

ECON 326 • Industrial Organization • Spring 2023

Ryan Safner Associate Professor of Economics safner@hood.edu ryansafner/ioS23 ioS23.classes.ryansafner.com

Outline

Recall: The Firm's Two Problems

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Total Profit As R(q)−C(q)R(q)−C(q)

Visualizing Profit Per Unit As MR(q)MR(q) and MC(q)MC(q)

Visualizing Profit Per Unit As MR(q)MR(q) and MC(q)MC(q)

Visualizing Profit Per Unit As MR(q)MR(q) and MC(q)MC(q)

Comparative Statics

If Market Price Changes I

If Market Price Changes II

The Firm’s Supply Curve

Calculating Profit

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Calculating (Average) Profit as AR(q)-AC(q)

Ryan Safner
Associate Professor of Economics
safner@hood.edu
ryansafner/ioS23
ioS23.classes.ryansafner.com

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

Ryan Safner
Associate Professor of Economics
safner@hood.edu
ryansafner/ioS23
ioS23.classes.ryansafner.com

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Total Profit As $R (q) - C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$

Visualizing Profit Per Unit As $M R (q)$ and $M C (q)$