Description Usage Arguments Details Value References See Also Examples
The function provides the Pdot-approximation simulation.
1 |
pdotcoeff |
An approximation result from |
stock |
An array of stock |
sdot |
An array of ds/dt, \dot{s}=\frac{ds}{dt} |
dsdotds |
An array of d(sdot)/ds, \frac{d \dot{s}}{d s} |
wval |
An array of W-value |
dwds |
An array of dw/ds, \frac{dW}{ds} |
Let \hat{β} be the vector of approximation coefficents from the results of pdotaprox
function.
The estimated shadow price (accounting) price of stock over the given approximation interval of
s \in [a,b], \hat{p} can be calculated as:
\hat{p} = \frac{ W_{s} + \mathbf{μ β} }{ δ - \dot{s}_{s} } .
The estimated value function is:
\hat{V} = \frac{1}{δ} ≤ft( W + \hat{p} \dot{s} \right) .
For more detils see Fenichel and Abbott (2014) and Fenichel et al. (2016).
A list of approximation resuts: shadow (accounting) prices, inclusive wealth, and value function, stock, and W values. Use results$item
(or results[["item"]]
) to import each result item.
shadowp |
Shadow price |
vfun |
Value function |
stock |
Stock |
wval |
W-value |
Fenichel, Eli P. and Joshua K. Abbott. (2014) "Natural Capital: From Metaphor to Measurement."
Journal of the Association of Environmental Economists. 1(1/2):1-27.
Fenichel, Eli P., Joshua K. Abbott, Jude Bayham, Whitney Boone, Erin M. K. Haacker, and Lisa Pfeiffer. (2016) "Measuring the Value of Groundwater and Other Forms of Natural Capital."
Proceedings of the National Academy of Sciences .113:2382-2387.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ## 1-D Reef-fish example: see Fenichel and Abbott (2014)
data("GOM")
nodes <- chebnodegen(param$nodes,param$lowerK,param$upperK)
simuDataPdot <- cbind(nodes,sdot(nodes,param),
dsdotds(nodes,param),dsdotdss(nodes,param),
dwds(nodes,param),dwdss(nodes,param))
Aspace <- aproxdef(param$order,param$lowerK,param$upperK,param$delta)
pdotC <- pdotaprox(Aspace,simuDataPdot[,1],simuDataPdot[,2],
simuDataPdot[,3],simuDataPdot[,4],
simuDataPdot[,5],simuDataPdot[,6])
GOMSimPdot <- pdotsim(pdotC,simuDataPdot[,1],simuDataPdot[,2],simuDataPdot[,3],
profit(nodes,param),simuDataPdot[,5])
# Shadow Price
plotgen(GOMSimPdot, xlabel="Stock size, s", ylabel="Shadow price")
# Value function and profit
plotgen(GOMSimPdot,ftype="vw",
xlabel="Stock size, s",
ylabel=c("Value Function","Profit"))
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