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Example Model
Austin Drenski edited this page Feb 6, 2017
·
34 revisions
This example looks at the effect of a 5 % price shock on one supplier in a sector where four suppliers initially have equal market shares.
-------------------
| Retail |
-------------------
/ / \ \
/ / \ \
/ / \ \
/ / \ \
----------- ----------- ----------- -----------
|Supplier1| |Supplier2| |Supplier3| |Supplier4|
----------- ----------- ----------- -----------
| Parameter | Value |
|---|---|
| Elasticity of substitution | 4.00 |
| Elasticity of supply | 5.00 |
| Elasticity of demand | -1.00 |
| Initial price | 1.00 |
| Market share | 0.25 |
| Shock (only Supplier3) | 0.05 |
| Supplier | ProducerPrice | ConsumerPrice | ConsumerPriceIndex |
|---|---|---|---|
| Retail | 1.0099 | ||
| Supplier1 | 1.0032 | 1.0032 | |
| Supplier2 | 1.0032 | 1.0032 | |
| Supplier3 | 0.9817 | 1.0308 | |
| Supplier4 | 1.0032 | 1.0032 |
using System;
using System.IO;
using System.Linq;
using System.Xml;
using System.Xml.Linq;
using AD.IO;
using AD.PartialEquilibriumApi.Optimization;
namespace AD.PartialEquilibriumApi.Example
{
public static class Example
{
public static void Example1()
{
XmlFilePath structureFile = CreateTempXmlFile();
DelimitedFilePath dataFile = CreateTempCsvFile();
// Read in the model and the data.
XElement model = CreateModelFromFile(structureFile, dataFile);
//XElement model = CreateModelFromInteractive(dataFile);
// Set the consumer prices.
model.SetConsumerPrices(model.DescendantsAndSelf()
.Select(x => x.InitialPrice())
.ToArray());
// Apply the price shocks.
model.ShockAllProducerPrices();
// Calculate the price indices.
model.CalculateConsumerPriceIndex();
// Calculate the market equilibrium starting on the root.
model.CalculateRootMarketEquilibrium();
// Create boolean vector indicating which nodes (in document-order) are variable.
bool[] variables =
new bool[]
{
false,
true,
true,
true,
true
};
// Create the objective function.
Func<double[], double> objectiveFunction =
x =>
{
// Update consumer prices to the argument vector.
// Result: x[i] if variables[i] is true
model.SetConsumerPrices(x, variables);
// Shock the current prices:
// Result: currentPrice * (1 + shock)
model.ShockAllProducerPrices();
// Calculate a price index for the sector:
// Result: [Σ marketShare[i] * (price[i] ^ (1 - elasticityOfSubstitution[i])] ^ [1 / (1 - elasticityOfSubstitution)]
model.CalculateConsumerPriceIndex();
// Caclulate the market equilibrium. Zero means equilibrium.
// [shockedPrice ^ elasticityOfSupply] - [(priceIndex ^ (elasticityOfSubstitution + elasticityOfDemand)) / (initialPrice ^ elasticityOfSubstitution)]
model.CalculateRootMarketEquilibrium();
// Return the sector's equilibrium value to the caller.
return model.MarketEquilibrium();
};
// Set up the simplex solver.
Simplex simplex =
new Simplex(
objectiveFunction: x => objectiveFunction(x),
lowerBound: 0,
upperBound: 100,
dimensions: 5,
numberOfSolutions: 5,
iterations: 1000,
textWriter: Console.Out);
// Find the minimum solution.
Solution solution = simplex.Minimize();
// Update the XML tree one more time with the optimal result.
double[] result = solution.Vector;
model.SetConsumerPrices(result, variables);
model.ShockAllProducerPrices();
model.CalculateConsumerPriceIndex();
model.CalculateRootMarketEquilibrium();
// Calculate new market shares
model.CalculateAllFinalMarketShares();
// Print the results.
Console.WriteLine("-----------------------------------------------------------------------------------------");
XmlWriterSettings settings = new XmlWriterSettings
{
Encoding = Encoding.UTF8,
Indent = true,
NewLineOnAttributes = true,
IndentChars = " "
};
using (XmlWriter writer = XmlWriter.Create(Console.Out, settings))
{
model.WriteTo(writer);
}
Console.WriteLine();
Console.WriteLine("-----------------------------------------------------------------------------------------");
Console.ReadLine();
}
private static XElement CreateModelFromFile(XmlFilePath structureFile, DelimitedFilePath dataFile)
{
return XElement.Load(structureFile)
.DefineAttributeData(dataFile);
}
private static XmlFilePath CreateTempXmlFile()
{
string xml = Path.ChangeExtension(Path.GetTempFileName(), ".xml");
using (StreamWriter writer = new StreamWriter(xml))
{
writer.WriteLine(
@"<Retail>
<Supplier1 />
<Supplier2 />
<Supplier3 />
<Supplier4 />
</Retail>");
}
return new XmlFilePath(xml);
}
private static DelimitedFilePath CreateTempCsvFile()
{
string csv = Path.ChangeExtension(Path.GetTempFileName(), ".csv");
using (StreamWriter writer = new StreamWriter(csv))
{
writer.WriteLine("ElasticityOfSubstitution,ElasticityOfSupply,ElasticityOfDemand,InitialPrice,InitialMarketShare,Shock");
writer.WriteLine("4,5,-1,1.0,1.00,0.00");
writer.WriteLine("4,5,-1,1.0,0.25,0.00");
writer.WriteLine("4,5,-1,1.0,0.25,0.00");
writer.WriteLine("4,5,-1,1.0,0.25,0.05");
writer.WriteLine("4,5,-1,1.0,0.25,0.00");
}
return new DelimitedFilePath(csv, ',');
}
}> i = 0: [ 2.9191e01, 4.6731e01, 6.3266e01, 4.6951e01, 9.8215e01 ] = 7.3285e17
> i = 10: [ 2.0871e01, 6.3110e00, 2.8254e01, 2.4324e01, 3.6187e01 ] = 2.8723e14
> i = 20: [ 1.5218e01, 2.5642e01, 1.6444e01, 1.3909e01, 1.2137e01 ] = 1.2472e14
> i = 30: [ 1.5218e01, 1.9188e01, 1.7190e01, 8.0037e00, 1.5040e01 ] = 8.8153e12
> i = 40: [ 1.5218e01, 1.9188e01, 1.7190e01, 8.0037e00, 1.5040e01 ] = 8.8153e12
> i = 50: [ 1.6471e01, 1.8020e01, 1.6955e01, 9.8264e00, 1.4551e01 ] = 6.2931e12
> i = 60: [ 1.6799e01, 1.7953e01, 1.4754e01, 7.9602e00, 1.5202e01 ] = 5.5694e12
> i = 70: [ 1.5452e01, 1.6067e01, 1.2161e01, 3.2924e00, 1.7982e01 ] = 1.9658e12
> i = 80: [ 1.2798e01, 1.4553e01, 8.3466e00, 1.3129e01, 2.2162e01 ] = 6.9731e11
> i = 90: [ 1.3456e01, 1.3415e01, 7.9699e00, 1.2167e01, 2.2189e01 ] = 4.5513e11
> i = 100: [ 1.2455e01, 1.2848e01, 7.7077e00, 1.1784e01, 2.3291e01 ] = 2.6452e11
> i = 110: [ 5.7413e00, 8.8984e00, 5.2747e00, 5.6521e00, 3.1002e01 ] = 3.1950e09
> i = 120: [ 8.5978e-01, 2.7922e00, 1.8091e00, 2.6156e-01, 3.8426e01 ] = 2.9256e04
> i = 130: [ 8.5978e-01, 2.7922e00, 1.8091e00, 2.6156e-01, 3.8426e01 ] = 2.9256e04
> i = 140: [ 8.5978e-01, 2.7922e00, 1.8091e00, 2.6156e-01, 3.8426e01 ] = 2.9256e04
> i = 150: [ 1.3789e00, 5.5558e-01, 3.3286e-01, 1.7819e-01, 3.9862e01 ] = 3.8392e02
> i = 160: [ 1.3789e00, 5.5558e-01, 3.3286e-01, 1.7819e-01, 3.9862e01 ] = 3.8392e02
> i = 170: [ 1.3789e00, 5.5558e-01, 3.3286e-01, 1.7819e-01, 3.9862e01 ] = 3.8392e02
> i = 180: [ 1.3789e00, 5.5558e-01, 3.3286e-01, 1.7819e-01, 3.9862e01 ] = 3.8392e02
> i = 190: [ 1.3789e00, 5.5558e-01, 3.3286e-01, 1.7819e-01, 3.9862e01 ] = 3.8392e02
> i = 200: [ 1.3789e00, 5.5558e-01, 3.3286e-01, 1.7819e-01, 3.9862e01 ] = 3.8392e02
> i = 210: [ 1.2956e00, 7.5734e-01, 1.0807e00, 6.4949e-01, 3.9285e01 ] = 2.3582e01
> i = 220: [ 1.2956e00, 7.5734e-01, 1.0807e00, 6.4949e-01, 3.9285e01 ] = 2.3582e01
> i = 230: [ 1.2956e00, 7.5734e-01, 1.0807e00, 6.4949e-01, 3.9285e01 ] = 2.3582e01
> i = 240: [ 1.2956e00, 7.5734e-01, 1.0807e00, 6.4949e-01, 3.9285e01 ] = 2.3582e01
> i = 250: [ 1.2956e00, 7.5734e-01, 1.0807e00, 6.4949e-01, 3.9285e01 ] = 2.3582e01
> i = 260: [ 1.2956e00, 7.5734e-01, 1.0807e00, 6.4949e-01, 3.9285e01 ] = 2.3582e01
> i = 270: [ 8.7920e-01, 6.8873e-01, 1.1177e00, 6.1521e-01, 3.9410e01 ] = 1.2206e01
> i = 280: [ 9.5244e-01, 7.9167e-01, 1.1684e00, 6.8653e-01, 3.9258e01 ] = 9.3677e00
> i = 290: [ 1.0415e00, 8.7920e-01, 1.2136e00, 7.7859e-01, 3.9040e01 ] = 7.3464e00
> i = 300: [ 1.0099e00, 9.6487e-01, 1.2290e00, 8.1786e-01, 3.8940e01 ] = 6.0237e00
> i = 310: [ 1.0864e00, 1.0352e00, 1.2190e00, 8.9289e-01, 3.8711e01 ] = 4.5238e00
> i = 320: [ 9.8136e-01, 1.0473e00, 1.1705e00, 9.0105e-01, 3.8631e01 ] = 2.5033e00
> i = 330: [ 1.0202e00, 1.0300e00, 1.1691e00, 1.0379e00, 3.8228e01 ] = 1.2066e00
> i = 340: [ 9.6520e-01, 1.0621e00, 1.1201e00, 1.0195e00, 3.8227e01 ] = 8.8776e-01
> i = 350: [ 1.0001e00, 1.0611e00, 1.1290e00, 1.0319e00, 3.8202e01 ] = 7.5197e-01
> i = 360: [ 1.0166e00, 1.0725e00, 1.1158e00, 1.0207e00, 3.8221e01 ] = 6.4910e-01
> i = 370: [ 1.0223e00, 1.0679e00, 1.1167e00, 1.0306e00, 3.8193e01 ] = 6.0864e-01
> i = 380: [ 1.0499e00, 1.0665e00, 1.0988e00, 1.0370e00, 3.8156e01 ] = 5.0399e-01
> i = 390: [ 1.0163e00, 1.0654e00, 1.0486e00, 1.0037e00, 3.8198e01 ] = 2.8355e-01
> i = 400: [ 1.0193e00, 1.0580e00, 1.0396e00, 1.0169e00, 3.8150e01 ] = 2.0866e-01
> i = 410: [ 1.0002e00, 1.0511e00, 1.0339e00, 1.0049e00, 3.8178e01 ] = 1.7239e-01
> i = 420: [ 9.9290e-01, 1.0444e00, 1.0261e00, 1.0057e00, 3.8167e01 ] = 1.4603e-01
> i = 430: [ 9.8898e-01, 1.0311e00, 1.0293e00, 1.0172e00, 3.8136e01 ] = 9.1712e-02
> i = 440: [ 9.9755e-01, 1.0161e00, 1.0387e00, 1.0281e00, 3.8115e01 ] = 5.5867e-02
> i = 450: [ 1.0048e00, 1.0164e00, 1.0442e00, 1.0290e00, 3.8118e01 ] = 5.1599e-02
> i = 460: [ 1.0051e00, 1.0195e00, 1.0380e00, 1.0273e00, 3.8117e01 ] = 4.7991e-02
> i = 470: [ 1.0063e00, 1.0132e00, 1.0367e00, 1.0258e00, 3.8119e01 ] = 3.5348e-02
> i = 480: [ 1.0130e00, 1.0054e00, 1.0403e00, 1.0150e00, 3.8156e01 ] = 1.3933e-02
> i = 490: [ 1.0122e00, 1.0062e00, 1.0396e00, 1.0129e00, 3.8161e01 ] = 1.0295e-02
> i = 500: [ 1.0107e00, 1.0028e00, 1.0319e00, 1.0061e00, 3.8173e01 ] = 3.9700e-03
> i = 510: [ 1.0092e00, 1.0052e00, 1.0334e00, 1.0063e00, 3.8173e01 ] = 2.4077e-03
> i = 520: [ 1.0029e00, 1.0049e00, 1.0300e00, 1.0036e00, 3.8177e01 ] = 2.7907e-04
> i = 530: [ 1.0038e00, 1.0036e00, 1.0318e00, 1.0031e00, 3.8181e01 ] = 6.4543e-05
> i = 540: [ 1.0036e00, 1.0034e00, 1.0311e00, 1.0032e00, 3.8180e01 ] = 1.1306e-05
> i = 550: [ 1.0032e00, 1.0033e00, 1.0308e00, 1.0032e00, 3.8179e01 ] = 1.5583e-06
> i = 560: [ 1.0034e00, 1.0033e00, 1.0308e00, 1.0033e00, 3.8179e01 ] = 7.6830e-07
> i = 570: [ 1.0033e00, 1.0032e00, 1.0308e00, 1.0033e00, 3.8179e01 ] = 1.5024e-07
> i = 580: [ 1.0033e00, 1.0033e00, 1.0308e00, 1.0033e00, 3.8179e01 ] = 5.4235e-08
> i = 590: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.9210e-08
> i = 600: [ 1.0033e00, 1.0033e00, 1.0308e00, 1.0033e00, 3.8179e01 ] = 8.5378e-09
> i = 610: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 4.0556e-09
> i = 620: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.1087e-10
> i = 630: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 3.6298e-11
> i = 640: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 7.5108e-12
> i = 650: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 7.5338e-13
> i = 660: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7234e-13
> i = 670: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 7.3639e-14
> i = 680: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.7048e-14
> i = 690: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 3.5010e-15
> i = 700: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 9.2075e-16
> i = 710: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 4.0725e-16
> i = 720: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.5618e-16
> i = 730: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 9.8858e-17
> i = 740: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.8622e-17
> i = 750: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.4852e-17
> i = 760: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 4.0164e-18
> i = 770: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.8271e-19
> i = 780: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.9178e-20
> i = 790: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 4.6985e-21
> i = 800: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 5.7695e-22
> i = 810: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.2424e-22
> i = 820: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.9649e-23
> i = 830: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 4.0499e-24
> i = 840: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 9.0473e-25
> i = 850: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.8120e-25
> i = 860: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.9279e-27
> i = 870: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 2.9279e-27
> i = 880: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.1672e-27
> i = 890: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7523e-28
> i = 900: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 4.2007e-29
> i = 910: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
> i = 920: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
> i = 930: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
> i = 940: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
> i = 950: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
> i = 960: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
> i = 970: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
> i = 980: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
> i = 990: [ 1.0033e00, 1.0033e00, 1.0309e00, 1.0033e00, 3.8179e01 ] = 1.7749e-30
-----------------------------------------------------------------------------------------
<?xml version="1.0" encoding="IBM437"?>
<Retail
ElasticityOfSubstitution="4"
ElasticityOfSupply="5"
ElasticityOfDemand="-1"
InitialPrice="1"
ConsumerPrice="1"
InitialMarketShare="1"
Shock="0"
ProducerPrice="1"
ConsumerPriceIndex="1.0099076384845791"
MarketEquilibrium="1.7749370367472766E-30"
FinalMarketShare="1">
<Supplier1
ElasticityOfSubstitution="4"
ElasticityOfSupply="5"
ElasticityOfDemand="-1"
InitialPrice="1"
ConsumerPrice="1.0032916989904535"
InitialMarketShare="0.25"
Shock="0"
ProducerPrice="1.0032916989904535"
ConsumerPriceIndex="0.247547389952549"
MarketEquilibrium="6.6613381477509392E-16"
FinalMarketShare="0.25497835956737486" />
<Supplier2
ElasticityOfSubstitution="4"
ElasticityOfSupply="5"
ElasticityOfDemand="-1"
InitialPrice="1"
ConsumerPrice="1.0032916989904535"
InitialMarketShare="0.25"
Shock="0"
ProducerPrice="1.0032916989904535"
ConsumerPriceIndex="0.247547389952549"
MarketEquilibrium="6.6613381477509392E-16"
FinalMarketShare="0.25497835956737486" />
<Supplier3
ElasticityOfSubstitution="4"
ElasticityOfSupply="5"
ElasticityOfDemand="-1"
InitialPrice="1"
ConsumerPrice="1.0308584894302912"
InitialMarketShare="0.25"
Shock="0.05"
ProducerPrice="0.98176998993361064"
ConsumerPriceIndex="0.22821429957986097"
MarketEquilibrium="-6.6613381477509392E-16"
FinalMarketShare="0.2350649212978754" />
<Supplier4
ElasticityOfSubstitution="4"
ElasticityOfSupply="5"
ElasticityOfDemand="-1"
InitialPrice="1"
ConsumerPrice="1.0032916989904535"
InitialMarketShare="0.25"
Shock="0"
ProducerPrice="1.0032916989904535"
ConsumerPriceIndex="0.247547389952549"
MarketEquilibrium="6.6613381477509392E-16"
FinalMarketShare="0.25497835956737486" />
</Retail>
-----------------------------------------------------------------------------------------