• \(\color{green}{\pi(q)}=\color{blue}{R(q)}-\color{red}{C(q)}\)

• \(\color{green}{\pi(q)}=\color{blue}{R(q)}-\color{red}{C(q)}\)

• \(\color{green}{\pi(q)}=\color{blue}{R(q)}-\color{red}{C(q)}\)

• Graph: find \(q^*\) to max \(\pi \implies q^*\) where max distance between \(R(q)\) and \(C(q)\)

• \(\color{green}{\pi(q)}=\color{blue}{R(q)}-\color{red}{C(q)}\)

• Graph: find \(q^*\) to max \(\pi \implies q^*\) where max distance between \(R(q)\) and \(C(q)\)

• Slopes must be equal: $$\color{blue}{MR(q)}=\color{red}{MC(q)}$$

• \(\color{green}{\pi(q)}=\color{blue}{R(q)}-\color{red}{C(q)}\)

• Graph: find \(q^*\) to max \(\pi \implies q^*\) where max distance between \(R(q)\) and \(C(q)\)

• Slopes must be equal: $$\color{blue}{MR(q)}=\color{red}{MC(q)}$$

• At low output \(q<q^*\), can increase \(\pi\) by producing more: \(\color{blue}{MR(q)}>\color{red}{MC(q)}\)

• At high output \(q>q^*\), can increase \(\pi\) by producing less: \(\color{blue}{MR(q)}<\color{red}{MC(q)}\)

• \(\pi\) is maximized where \(\color{blue}{MR(q)}=\color{red}{MC(q)}\)

• Suppose the market price increases

• Firm (always setting MR=MC) will respond by producing more

• Suppose the market price decreases

• Firm (always setting MR=MC) will respond by producing less

• The firm’s marginal cost curve is its supply curve^‡ $$\color{red}{p=MC(q)}$$
  • 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

• Profit is $$\pi(q)=R(q)-C(q)$$

• Profit is $$\pi(q)=R(q)-C(q)$$

• Profit per unit can be calculated as: $$\begin{align*} \frac{\pi(q)}{q}&=\color{blue}{AR(q)}-\color{orange}{AC(q)}\\ &=\color{blue}{p}-\color{orange}{AC(q)}\\ \end{align*}$$

• Profit is $$\pi(q)=R(q)-C(q)$$

• Profit per unit can be calculated as: $$\begin{align*} \frac{\pi(q)}{q}&=\color{blue}{AR(q)}-\color{orange}{AC(q)}\\ &=\color{blue}{p}-\color{orange}{AC(q)}\\ \end{align*}$$

• Multiply by \(q\) to get total profit: $$\pi(q)=q\left[\color{blue}{p}-\color{orange}{AC(q)} \right]$$

• At market price of p* = $10

• At q* = 5 (per unit):

• At q* = 5 (totals):

• At market price of p* = $10

• At q* = 5 (per unit):

  • AR(5) = $10/unit

• At q* = 5 (totals):

  • R(5) = $50

• 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

• At market price of p* = $10

• At q* = 5 (per unit):

  • AR(5) = $10/unit
  • AC(5) = $7/unit
  • A\(\pi\)(5) = $3/unit

• At q* = 5 (totals):

  • R(5) = $50
  • C(5) = $35
  • \(\pi\) = $15

• At market price of p* = $2

• At q* = 1 (per unit):

• At q* = 1 (totals):

• At market price of p* = $2

• At q* = 1 (per unit):

  • AR(1) = $2/unit

• At q* = 1 (totals):

  • R(1) = $2

• 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

• At market price of p* = $2

• At q* = 1 (per unit):

  • AR(1) = $2/unit
  • AC(1) = $10/unit
  • A\(\pi\)(1) = -$8/unit

• At q* = 1 (totals):

  • R(1) = $2
  • C(1) = $10
  • \(\pi\)(1) = -$8

• What if a firm's profits at \(q^*\) are negative (i.e. it earns losses)?

• Should it produce at all?

• Suppose firm chooses to produce nothing \((q=0)\):

• If it has fixed costs \((f>0)\), its profits are:

$$\begin{align*} \pi(q)&=pq-C(q)\\ \end{align*}$$

• Suppose firm chooses to produce nothing \((q=0)\):

• If it has fixed costs \((f>0)\), its profits are:

$$\begin{align*} \pi(q)&=pq-\color{red}{C(q)}\\ \pi(q)&=pq-\color{red}{f-VC(q)}\\ \end{align*}$$

• Suppose firm chooses to produce nothing \((q=0)\):

• If it has fixed costs \((f>0)\), its profits are:

$$\begin{align*} \pi(q)&=pq-C(q)\\ \pi(q)&=pq-f-VC(q)\\ \pi(0)&=-f\\ \end{align*}$$

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

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

$$\begin{align*} \pi \text{ from producing} &< \pi \text{ from not producing}\\ \end{align*}$$

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

$$\begin{align*} \pi \text{ from producing} &< \pi \text{ from not producing}\\ \pi(q) &< -f \\ \end{align*}$$

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

$$\begin{align*} \pi \text{ from producing} &< \pi \text{ from not producing}\\ \pi(q) &< -f \\ pq-VC(q)-f &<-f\\ \end{align*}$$

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

$$\begin{align*} \pi \text{ from producing} &< \pi \text{ from not producing}\\ \pi(q) &< -f \\ pq-VC(q)-f &<-f\\ pq-VC(q) &< 0\\ \end{align*}$$

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

$$\begin{align*} \pi \text{ from producing} &< \pi \text{ from not producing}\\ \pi(q) &< -f \\ pq-VC(q)-f &<-f\\ pq-VC(q) &< 0\\ pq &< VC(q)\\ \end{align*}$$

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

$$\begin{align*} \pi \text{ from producing} &< \pi \text{ from not producing}\\ \pi(q) &< -f \\ pq-VC(q)-f &<-f\\ pq-VC(q) &< 0\\ pq &< VC(q)\\ \color{red}{p} & \color{red}{<} \color{red}{AVC(q)}\\ \end{align*}$$

• Shut down price: firm will shut down production in the short run when \(p<AVC(q)\)