This week I prepared another example to teach economic modelling.

Fisheries play a minor role in the economy of Germany, corresponding to only 5% of total EU production. However, small-scale fishing is still an important activity in Germany’s coastal regions and some inland areas, employing more than 40,000 people and about 1500 vessels (Centenera, 2014; Döring et al., 2020). In many regions, fisheries have shaped the population, environment, cultural heritage, social cohesion and identity. Many fishers express a deep attachment to their occupational identity (Oleson et al., 2015; Urquhart et al., 2014a).

In this exercise, students take the perspective of the German government managing the stocks of the Baltic Sea. Both commercial as well as the small-scale fishery (SSF) fleet use the same quota, which has to be distributed to the two fleets. The choice of the German government is what percentage of the quota is assigned to commercial and to SSF. The objective is to maximize social welfare, which for now is simply the sum of profit of the two fleets.

Instead of effort, we set up the problem in terms of harvest. A starting point of this exercise could be to write the welfare maximisation formula for the German government in R:

```
# Welfare maximization
Welfare[t] <- (Value_commercial - Costs_commercial + Value_SSF - Costs_SSF)/((1+discountfactor)^t)
sum(Welfare)
```

The parameters *Value_commercial* and *Value_SSF* need to be defined. They should be a function of the harvest for each fishery: the higher the harvest, the higher the revenues for the fishery.

Doring et al. (2020) report some useful statistics for the fishery fleet and SSF fleet in Germany, including the value in million EUR, quantity fished (in tonnes). In 2015, the value of the landing for the SSF was 61 million EUR for 35000 ton of landings, and 226 million EUR for 238000 tons of landings. This means that the commercial scale fisheries correspond to a value of 165 million EUR and a quantity of 203000 tons.

In this exercise, I assume that the ratio of value to quantity harvested is fixed for both commercial and SSF. This means that, for each unit harvested, the fishery gets a fixed revenue/value. For example, for commercial fisheries:

So I can rewrite the commercial value of commercial fisheries as: .

The commercial value of SSF is: .

So I can change the welfare function in R.

```
# Welfare maximization
Welfare[t] <- (812.8079*harvest_CF - Costs_commercial + 1742.857*harvest_SSF - Costs_SFF)/((1+discountfactor)^t)
sum(Welfare)
```

The second part is to change the cost functions in the welfare function. Since we are writing everything in terms of harvest, we can change the welfare function accounting for both the catchability coefficient and the cost per unit of effort, as well as a Biomass function:

```
Welfare[t] <- (812.8079*harvest_CF[t] - cost_CF *(harvest_CF[t] /q_CF) *(Biomass[t]^(-rho)) +
1742.857*harvest_SSF[t] - cost_SSF*(harvest_SSF[t]/q_SSF)*(Biomass[t]^(-rho)))/((1+discountfactor)^t)
```

Finally, to get the function to work, we need reasonable values for the parameters of the function. These are made-up, rather than ground on reality:

```
# Parameters
cost_CF <- 4000
cost_SSF <- 12000
discountfactor <- 0.05
rho <- 1
q_CF <- 0.00001 # Catchability coefficient
q_SSF <- 0.000001 # Catchability coefficient
k <- 1
r <- 1
timeframe <- 20
harvest_CF <- c(rep(0, times = timeframe))
harvest_SSF <- c(rep(0, times = timeframe))
Welfare <- c(rep(0, times = timeframe))
Biomass <- c(rep(1000000, times = timeframe))
quota <- c(rep(1000, times = timeframe))
```

Finally, I created a function called welfare_max that includes: 1) a loop forcing the harvest of SSF to be the catch quota minus the commercial fishery’s catch; 2) a loop defining the biomass at each time period (for t>1); and 3) the welfare function as I defined above.

```
welfare_max <- function(harvest_CF){
for(t in 1:timeframe){
harvest_SSF[t] <- quota[t]-harvest_CF[t] }
for(t in 2:(timeframe-1)){Biomass[t] <- Biomass[t-1]+r*Biomass[t-1]*(1-Biomass[t-1]/k)+(harvest_SSF[t-1]+harvest_CF[t-1]) }
for(t in 1:timeframe){
Welfare[t] <- (812.8079*harvest_CF[t] - cost_CF*(harvest_CF[t]/q_CF)*(Biomass[t]^(-rho)) + 1742.857*harvest_SSF[t] - cost_SSF*(harvest_SSF[t]/q_SSF)*(Biomass[t]^(-rho)))/((1+discountfactor)^t)
}
return(sum(Welfare))
}
```

Instead of optimizing this function, I just want to see how profit changes with different harvest distributions. Let us say that the Government has 1000 units of harvest of annual quota, and wants to see how welfare changes when commercial fisheries get 100%, 50% or 0% of this quota. I can assess that with the function alone:

```
> welfare_max(c(rep(1000, times = timeframe))) # Change value of harvest for CF
[1] 9597675
> welfare_max(c(rep(500, times = timeframe))) # Change value of harvest for CF
[1] 7683146
> welfare_max(c(rep(0, times = timeframe))) # Change value of harvest for CF
[1] 5768616
```

According to these numbers, the highest welfare is when commercial fisheries get 100% of the quota (first line). This is because the parameter values were set in such a way to make SSF quite costly, while commercial fisheries have lower costs.

Next, I want to account for the fact that SSF have important values beyond fishing. In our forthcoming paper, Ceccaci et al. (2023) find that SSF has an important recreational value. This means that visitors are willing to pay to visit places where SSF vessels are present. The authors report that each German citizen visits blue spaces 42.5 times a year and each vessel has a recreational value of 0.0019 per person and per visit.

Doring et al. (2020) also report the number of vessels in 2015: 1470 for the SSF and 1520 in total, meaning the commercial fisheries had around 50 vessels. Again, we assume that the harvest per vessel value needs to be fixed (the ratio is 23.80952), so that the number of active vessels is a function of the harvest allocated to SSF.

For the sake of this exercise, I assume that each SSF vessel has a value of: . So I can add this value in the welfare maximization function and do the same comparison as before:

```
welfare_max <- function(harvest_CF){
for(t in 1:timeframe){
harvest_SSF[t] <- quota[t]-harvest_CF[t] }
for(t in 2:(timeframe-1)){Biomass[t] <- Biomass[t-1]+r*Biomass[t-1]*(1-Biomass[t-1]/k)+(harvest_SSF[t-1]+harvest_CF[t-1]) }
for(t in 1:timeframe){
Welfare[t] <- (812.8079*harvest_CF[t] - cost_CF*(harvest_CF[t]/q_CF)*(Biomass[t]^(-rho)) +
1742.857*harvest_SSF[t] - cost_SSF*(harvest_SSF[t]/q_SSF)*(Biomass[t]^(-rho)) +
(harvest_SSF[t]/23.80952)*0.0019*84551543)/((1+discountfactor)^t)
}
return(sum(Welfare))
}
```

For 100%, 50% and 0% of harvest allocated to commercial fisheries, the welfare obtained is as follows:

```
> welfare_max(c(rep(1000, times = timeframe))) # Change value of harvest for CF
[1] 9597675
> welfare_max(c(rep(500, times = timeframe))) # Change value of harvest for CF
[1] 49725747
> welfare_max(c(rep(0, times = timeframe))) # Change value of harvest for CF
[1] 89853819
```

According to these results, the best thing the German government should be is to allocate 100% of the quota to SSF (89 million EUR). Despite using made-up values for the parameters, the message here is how welfare of a society can change based on government’s decisions and what kind of values are accounted for when decisions are made.

**References:**

Ceccacci, A., Lopes, A. F., Mulazzani, L., Malorgio, G. (forthcoming). Recreation in Coastal Environments: Estimating the Non-Market Value of Fishing Harbors. Working paper

Centenera, R. (2014). *Fisheries in Germany: In-Depth Analysis*. Policy Department European Union.

Döring, R., Berkenhagen, J., Hentsch, S., & K. (2020). Small-Scale Fisheries in Germany: A Disappearing Profession? In J. J. Pascual-Fernández, C. Pita, & M. Bavinck (Eds.), *Small-Scale Fisheries in Europe: Status, Resilience and Governance* (pp. 581–600). Springer Nature Switzerland AG.

Oleson, K. L. L., Barnes, M., Brander, L. M., Oliver, T. A., Van Beek, I., Zafindrasilivonona, B., & Van Beukering, P. (2015). Cultural bequest values for ecosystem service flows among indigenous fishers: A discrete choice experiment validated with mixed methods. *Ecological Economics*, *114*, 104–116. https://doi.org/10.1016/j.ecolecon.2015.02.028

Urquhart, J., Acott, T., & Zhao, M. (2013). Introduction: Social and cultural impacts of marine fisheries. *Marine Policy*, *37*(1), 1–2. https://doi.org/10.1016/j.marpol.2012.04.007