19 Industry Supply – A Microeconomic Theory Workbook

19.2 Classwork 19: Industry Supply

This classwork examines how individual firm supply curves combine into industry supply, and how firms entering or leaving affects long-run equilibrium. The key idea is that in the long run, free entry and exit mean firms can’t make economic profits or losses - they must break even.

Short-run supply: Let’s start with a simple market that has three producers with these supply curves:
- Firm 1: \(S_1(P) = P - 5\)
- Firm 2: \(S_2(P) = P - 10\)
- Firm 3: \(S_3(P) = P - 15\)
HINT: Remember that a firm’s supply curve shows how much it will produce at each price. When price is too low, the firm produces 0.

Let’s plot these supply curves. We’ll use stat_function() to draw them. Notice I want P on the y-axis and Q on the x-axis, but instead of rearranging the supply curves to solve for P, I’ll write them as functions of P and then use coord_flip().

library(tidyverse)

ggplot() +
  stat_function(fun = function(P) P - 5, aes(color = "Firm 1")) +
  stat_function(fun = function(P) ___, aes(color = "Firm 2")) +
  stat_function(fun = function(P) ___, aes(color = "Firm 3")) +
  xlim(0, 30) +
  ylim(0, 20) +
  xlab("P") +
  ylab("Q") +
  coord_flip()

Fill in the table to find the quantity supplied for each of these prices by each firm as well as the industry (market) in total.

Price	Firm 1 Supply	Firm 2 Supply	Firm 3 Supply	Industry Supply
6	P - 5 = 1	P - 10 < 0	P - 15 < 0	1
10	P - 5 = 5	P - 10 = 0	P - 15 < 0	5
12
16
20

Note that the industry supply curve is just the horizontal sum of the individual firm supply curves of those firms producing a positive amount. Find the industry supply curve algebraically (it will be a piece-wise function) and then use stat_function to plot the industry supply.

$$
S_I(P) = 
\begin{cases} 
  0 & \text{if } ___\\
  P - 5 & \text{if } 5 \leq P \lt 10 \\
  2 P - 15 & \text{if } ___\\
  3P - 30 & \text{if } ___
\end{cases}
$$

ggplot() +
  stat_function(fun = function(P) {
    case_when(
      P < 5 ~ 0,
      P < 10 ~ ___,
      P < 15 ~ ___,
      P >= 15 ~ ___
    )
  }) +
  ylim(0, 30) +
  xlim(0, 20) +
  xlab("P") +
  ylab("Q") +
  coord_flip()

Long-run equilibrium with free entry/exit: Suppose an industry has:

Market demand given by: \(P = 100 - Q\)
Each firm’s costs given by: \(C(q) = q^2 + 25\)
Free entry/exit (firms can freely enter or exit the market)

First, show that each firm’s supply curve is \(P = 2q\). HINTS: Remember supply curve = MC (marginal cost) above minimum AVC. To find MC: take the derivative of total cost. To find AVC: divide variable cost by q.
Show that the number of firms in long-run equilibrium is 18. HINTS: In a long-run equilibrium with free entry and exit, two conditions must hold: Market clears (supply = demand), and each firm earns zero economic profit (TR = TC). The second condition exists because if firms made positive profits, new firms would want to enter, which means more industry supply, which means the market price falls, which means profits fall. Eventually, economic profits erode to 0, in which case firms neither have an incentive to exit nor to enter: we have a stable equilibrium.
Find market price and quantity. HINTS: Once we know number of firms (n) and each firm’s output (q), we can find total market quantity: Q = n×q, and market price: either plug Q into demand curve or q into supply curve.

19.1 CW 18 Review

19.2 Classwork 19: Industry Supply