capn (version 1.0.0)

pdotsim: Simulation of Pdot-approximation

Description

The function provides the Pdot-approximation simulation.

Usage

pdotsim(pdotcoeff, stock, sdot, dsdotds, wval, dwds)

Arguments

pdotcoeff

An approximation result from pdotaprox function

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, \(\frac{dW}{ds}\)

Value

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

Details

Let \(\hat{\beta}\) 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:

\(\hat{p} = \frac{ W_{s} + \mathbf{\mu \beta} }{ \delta - \dot{s}_{s} } \).

The estimated value function is:

\( \hat{V} = \frac{1}{\delta} \left( W + \hat{p} \dot{s} \right) \).

For more detils see Fenichel and Abbott (2014) and Fenichel et al. (2016).

References

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.

See Also

pdotaprox

Examples

## 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"))