Data and Model Application

Quantifying the market effects demonstrated in our conceptual discussion requires translating the control-induced changes into numerical terms. As a result, the market model is expressed as a series of mathematical equations representing supply and demand in each affected market. The equations represent the relationship between market prices and the quantity supplied (or demanded).

Thus, we need data on market prices and quantities for each affected market as well as values for the mathematical parameters that quantify the relationship between market prices and the demand (or supply) responses.

Price and Quantity Data

The market price and quantity data for each of the Gulf states were gathered from secondary data sources. Chapter 2 explains details of the data collection process and descriptive statistics of the data. All

price and quantity values used in the model are for the summer period (April to October). The market model will generate post-control values for these values. Chapter 4 will report these values.

Model Parameters

To operate the market model the key model parameters must be set to appropriate values. Table 3-1 lists the key model parameters.

Chapter 2 provides specific values for most of these parameters.

The demand and supply parameters are discussed below. The impacts on and supply responses from the harvesting sector depend critically on the parameters associated with harvesting productivity (with and without the control options) and harvesting income. The supply function (for each producing region) is computed using these data and the method described below.

Because of significantly different harvesting conditions within the Gulf, we defined six distinct suppliers:

➤ Florida

➤ Alabama/Mississippi

➤ Louisiana small boats

➤ Louisiana medium boats

➤ Louisiana large boats

➤ Texas

Demand Function Estimation

Modeling demand responses to changes in price requires a demand function specific to Gulf oysters. This function was estimated econometrically using monthly time-series data for Gulf prices and quantities (National Marine Fisheries Service data) in a simultaneous equations framework. In addition to the Gulf oyster price, Gulf oyster demand was estimated as a function of Gulf income, Northeast U.S. oyster price, Pacific oyster price, and a time-trend variable.

The estimated value for the elasticity of Gulf demand with respect to Gulf price is approximately -1.1, meaning that the percentage change in the quantity of Gulf oysters demanded would be slightly higher than the percentage change in price. Our estimate is virtually identical to Cheng and Capps’ (1988) estimated

Table 3-1. Key Market Model Parameters

Baseline harvesting productivity Bags per day

Days per boat per season Number of workers per boat

Days per season spent maintaining lease Average round-trip time to/from beds Average time spent harvesting

Effects of time and temperature controls on harvesting productivity Percentage of summer under ISSC Level 4 (6 hour limit) Percentage of summer under ISSC Level 3 (12 hour limit)

Ratio of operating costs (e.g., gas, supplies) to total variable costs (including labor) Harvester income/expenses

Revenue Operating costs Depreciation

Labor “reservation” wage

Own-price supply parameter (computed from harvest productivity and income parameters) Own-price demand parameter (estimated with econometric model)

Shellstock demand shares

Percentage of summer output to halfshell market

elasticity for oysters. Cheng and Capps and other studies (Kearney, 1993) show that oyster demand is somewhat more elastic than the demand for other fish species. However, Thurman and Easley (1992) show more elastic demand for red drum (approximately -4.7) than we find for oysters.

Under the marketing restriction, the inward shift of the Gulf demand function is accomplished by reducing Gulf demand quantity by the amount of summer halfshell demand and assuming that the new

“shucked-only” demand function has the same relative price

responsiveness (elasticity) as the original demand function including both halfshell and shucked.

Supply Function Estimation

Estimating the supply function for a fishery product is notoriously difficult because of the inherent variability of supply conditions, particularly natural factors such as weather and/or population fluctuations (Kearney, 1993). Consequently, rather than estimate a supply function econometrically, we constructed supply functions using economic principles and the data provided to us in our site visits with harvesters.

Figure 3-7 Illustrates construction of the supply function for a particular region. The minimum “threshold” price, P^T, is the shellstock price at which the corresponding returns to harvesting labor are equal to the minimum wage. This threshold price implicitly assumes that no harvesting would be conducted if the returns to harvesting efforts were less than the minimum wage.

Q

Imputed Supply Fuction

P

Quantity

$/Unit

P^T = minimum

price

•

•

Observed Baseline Equilibrium

The region’s supply function is then constructed, graphically, by connecting a line from the threshold price on the vertical axis to the observed baseline equilibrium price and quantity (P,Q). The slope of this line suggests how elastic (responsive) supply is to changes in price. A flat slope indicates very responsive (elastic) supply and a steep slope indicates a relatively inelastic supply response.

Figure 3-7. Supply Curve Construction

The threshold prices are computed individually for each region based on the average daily boat yield and nonlabor cost data we obtained from site visits. In each case, these threshold prices are connected (via a mathematical equation) to the summer baseline price and quantity values to construct state-specific supply functions.

The post-control supply functions (in the case of the ISSC control option) are then modified to capture the alteration in daily yields obtainable with the time and temperature controls, which will raise the threshold price and shift up the supply function as illustrated in Figure 3-6. The post-control supply function for the Gulf is the sum of the separate supply functions for each region, as illustrated in Figure 3-4.

Model Solution

Each control option imposes a change in one or more of the markets in the system that translates to a change in the associated equations.

The change in the equation system means that a new set of prices and quantities provide the equilibrium solution to the system. The new solution is computed by iterating supply and demand responses until the new supply quantity equals the new demand quantity at the same price. The iterative solution algorithm is programmed directly into a spreadsheet software package. These new prices and quantities are then compared to the baseline prices and quantities to measure the change in these key values and thus drive the analysis of impacts.