# Collective Action, Market Access, and Competition: Evidence from Chilean Wine-Grape Markets

## Brent Hueth and Pilar Jano

### August 19, 2019

# Question

- Cooperatives exist. Why? (there are plenty of reasons they should not!)
- We find evidence with others that cooperatives service "high-cost" farmers?

Developing a theoretical framework to examine these questions.

# Monopoly

- A single firm facing $n$ consumers
- $D_i(p)$ is demand for each consumer $i$
- $k$ is fixed cost for the firm
- Marginal costs are zero
- $\pi(p) \equiv pD(p)$
- $\Pi(p) \equiv n \pi(p) - k$
- $p_m$ maximizes $\Pi(p)$
- $CS(p) \equiv \int_p^\infty D(t)dt$
- total surplus = $\Pi(p) + nCS(p)$

# Example

- $a$ = demand intercept
- $k$ = setup cost
- $n$ = number of farmers

$q = (a - p)$
$\Pi = q\times p$
$\Pi = n\times q\times p - k$
$\textrm{CS} = \frac{(a-p)^2}{2}$
$\textrm{S} = \Pi + n \textrm{CS}$

# Aside: Missing Market


# What frictions generate this outcome?

- Nonconvexity
- Information asymmetry
- Commitment and contract enforcement

### Responses to frictions can be public, private, or mix

- Responses involve some form of *collective action* (in democratic societies, perhaps indirectly through elected representives)
- Subject of on-going research

# For profit entry

- If post-entry play is Bertrand, there is no entry.
- If post-entry play is Cournot, the incumbent can limit entry with the quantity $n(a-2\sqrt{k}),$ (implying $p=2\sqrt{k}$)

# Entry by a "closed" cooperative

- "Closed" means that founders use an *ex ante* contract commiting to exclude non-founders

## Setup

- Consumers have access to technology with marginal cost $0< c < p_m$
- Consumers face setup cost $k$
- Only contributors/participants can purchase from the cooperative
- Incumbent offers price, $p_d$, anticipating response from consumers.
- Each consumer participates with probability $\rho(p_d)$ (endogenous)

## Timing

1. Each consumer chooses whether are not to participate in cooperative formation.
1. All participants share equally the starup cost, $k$, and pay marginal cost $c$ per-unit. Consumer surplus under cooperative formation is given by, $V_C(m) \equiv CS(c)-k/m$.
1. For given number of participants, $m$, the cooperative forms only if surplus for each member is higher than at current price or, $V_c(m)\geq CS(p_d)$.

# Solution

- Define $m^*(p_d) \equiv \min\left\{m : V_c(m) \geq CS(p_d)\right\}$
- Calculate the likelihood of observing a given $m$ as

$$P(\rho(p_d), m) = {{n-1}\choose{m-1}}\rho(p_d)^{m-1}(1-\rho(p_d))^{n-m}$$

- Total probability of entry is $P_e(p_d) \equiv \sum_{i=m^*(p_d)}^n P(\rho(p_d), i)$.
- Participating produces expected benefit $\Delta(\rho, p_d) = \sum_{i=m^*(p_d)}^n P(q, i)V_c(i) - CS(p_m)$
- The incumbent can exercise *probabilist deterrence* by lowering the pre-entry price (which lowers the total probability of entry)
- For given deterrence price, $p_d\in[c, p_m]$, expected profits for the incumbent are given by $$V_F(p_d)\equiv \sum_{i=m^*(p_d)}^n\left(P(\rho^*(p_d), i)(n-i)\pi(p_d)\right) + (1-P_e(p_d))n\pi(p_m) - k$$

# Equilibrium satisfies

- The incumbent firm choose $p^*_d$ to maximize $V_F(p_d)$ (charged to everyone if there is no entry)
- $\rho^*(p_d)$ solves $F^{-1}(\rho^*) = \Delta(\rho^*, p_d)$ (quantile response equilibrium)

# Entry by an open cooperative

- Is it *ex ante* beneficial to exclude non-contributors completely?
- Can treat them differentially
- One possibility is marginal cost pricing plus a share (possibly) all of founder contributions

## Consumer heterogeneity

- Why might "high-cost" consumers be more likely to be among member population?

# Entry by closed cooperative

- A coalition of $m$ consumers forms a "cooperative" to produce the good from themselves.
- The cooperative faces positive marginal cost $0<c<p_m$.
- Only contributors can purchase from the cooperative (if it forms successfully)
- Non-contributors must purchase at the monopoly price from the incumbent firm
- Consumer surplus with $m$ contributors is $V_c(m) \equiv CS(c)-k/m$
- For given price $p_d$, a cooperative forms only if $V_c(m) \geq CS(p_d)$.
- Define $m^*(p_d) \equiv \min\left\{m : V_c(m) \geq CS(p_d)\right\}$
- $\rho$ is the probability that an individual participates
- Probability that exactly $m-1$ persons participates is $P(\rho, m) = {{n-1}\choose{m-1}}\rho^{m-1}(1-\rho)^{n-m}$
- Then the expected difference between participating and not is $\Delta(\rho, p_d) = \sum_{i=m^*(p_d)}^n P(q, i)V_c(i) - CS(p_m)$
- A quantile response $\rho^*(p_d)$ equilibrium solves $F^{-1}(\rho^*) = \Delta(\rho^*, p_d)$
- We can can calculate the likelihood of observing a give $m$ as $P(\rho^*(p_d), m)$, and the total probability of entry as $P_e(p_d) \equiv \sum_{i=m^*(p_d)}^n P(\rho^*(p_d), i)$.
- The incumbent can exercise *probabilist deterrence* by lowering the pre-entry price (which lowers the total probability of entry)
- For given deterrence price, $p_d$, expected profits for the incumbent are given by $$\sum_{i=m^*(p_d)}^n\left(P(\rho^*(p_d), i)(n-i)\pi(p_d)\right) + (1-P_e(p_d))n\pi(p_m) - k$$