1 Grid States, Choices and Optimal Choices Example

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1.1Generate State Grid

There many multiple individuals, each individual’s value for each state space variable is different. We duplicate that by shockCount and choicecount:

stateCount = 2;
shockCount = 3;
choiceCount = 4;

state1 = rand(1,stateCount)

state1 = 1x2
0.0571    0.6694

states1ShkDup = state1(ones(shockCount*choiceCount,1),:)

states1ShkDup = 12x2
0.0571    0.6694
0.0571    0.6694
0.0571    0.6694
0.0571    0.6694
0.0571    0.6694
0.0571    0.6694
0.0571    0.6694
0.0571    0.6694
0.0571    0.6694
0.0571    0.6694

states1ShkDup(:)

ans = 24x1
0.0571
0.0571
0.0571
0.0571
0.0571
0.0571
0.0571
0.0571
0.0571
0.0571

1.2Generate Choices

Generate Choice Grid, Example: Each individual has minimal protein and maximal protein they can get Generate a evenly set grid of choices for each individual from min to max. Individual min and max choice is a function of some component of their state-space, such as wealth/income level, and choice is the quantity of good to purchase.

stateCount = 2;
shockCount = 3;
choiceCount = 4;

% 1. Min and Max Choices for each state
minprot_n = floor(rand(1,stateCount)*10)

minprot_n = 1x2
7     7

maxprot_n = minprot_n + floor(rand(1,stateCount)*10)

maxprot_n = 1x2
14    12

% 2. Choice Ratios, ratios of max-min difference
protChoiceGrid = linspace(0,1,choiceCount)

protChoiceGrid = 1x4
0    0.3333    0.6667    1.0000

% 3. Each column is a different state.
searchMatrix = (protChoiceGrid'*(maxprot_n-minprot_n)+minprot_n(ones(choiceCount,1),:))

searchMatrix = 4x2
7.0000    7.0000
9.3333    8.6667
11.6667   10.3333
14.0000   12.0000

% 4. Each column is a different state, each set of rows is a different shock% for the state. In this structure, shocks (to preference for example), do% not change choice grid for a given state
searchMatrix = searchMatrix([1:choiceCount]'* ones(1,shockCount), [1:stateCount]' * ones(1,1))

searchMatrix = 12x2
7.0000    7.0000
9.3333    8.6667
11.6667   10.3333
14.0000   12.0000
7.0000    7.0000
9.3333    8.6667
11.6667   10.3333
14.0000   12.0000
7.0000    7.0000
9.3333    8.6667

searchMatrix(:)

ans = 24x1
7.0000
9.3333
11.6667
14.0000
7.0000
9.3333
11.6667
14.0000
7.0000
9.3333

1.3Average Utility over Shocks

Average of Shocks, E(value) For each STATE and CHOICE, x number of shocks. Need to average over shocks; The raw value output is: STATES * SHOCKS * CHOICES; Code below turn into various things, see MATLAB CODE STRUCTURE in oneNOTE GCC working notes

shockCount = 2;
choiceCount = 3;
stateCount = 4;

% 1. VALUE vector (STATES * SHOCKS * CHOICES by 1), this is generated by utility% evaluation function that takes as input STATES, SHOCKS, and CHOICES
valuesOri = sort(rand(choiceCount*shockCount*stateCount,1))

valuesOri = 24x1
0.0296
0.1141
0.1472
0.1514
0.1826
0.1936
0.2526
0.2911
0.3257
0.3352

% 2. CHOICES by STATES * SHOCKS (ST1 SK1, ST1 SK2; ST2 SK1, etc), each% column are values for different choices given the same state and shock.
values = reshape(valuesOri,[choiceCount,shockCount*stateCount])

values = 3x8
0.0296    0.1514    0.2526    0.3352    0.5939    0.7065    0.8791    0.9204
0.1141    0.1826    0.2911    0.3480    0.5992    0.7267    0.9001    0.9508
0.1472    0.1936    0.3257    0.4578    0.6576    0.7792    0.9018    0.9658

% 3. SHOCKS by CHOICES * STATES (CH1 ST1, CH1 ST2; CH2 ST1, etc), each% column are two shocks for each state given the same choice. Note this% assumes that for different shocks of the same state choice vector is the% same.
values = reshape(values',[shockCount, choiceCount*stateCount])

values = 2x12
0.0296    0.2526    0.5939    0.8791    0.1141    0.2911    0.5992    0.9001    0.1472    0.3257    0.6576    0.9018
0.1514    0.3352    0.7065    0.9204    0.1826    0.3480    0.7267    0.9508    0.1936    0.4578    0.7792    0.9658

% 4. AVG: 1 by CHOICES * STATES (CH1 ST1, CH1 ST2; CH2 ST1, etc), take% average over shocks for each state and choice combo
valuesMn = mean(values,1)

valuesMn = 1x12
0.0905    0.2939    0.6502    0.8997    0.1483    0.3196    0.6629    0.9254    0.1704    0.3918    0.7184    0.9338

% 5. AVG: CHOICES * STATES. From this matrix, one can now pick maximum% utility, and match that to the index on choice vector
valuesMn = reshape(valuesMn, [stateCount, choiceCount])'

valuesMn = 3x4
0.0905    0.2939    0.6502    0.8997
0.1483    0.3196    0.6629    0.9254
0.1704    0.3918    0.7184    0.9338

1.4Pick Optimal Choice

choiceCount = 3;
stateCount = 4;

% 1. Matrix, each column is a state, each row is a choice
randMat = rand(choiceCount,stateCount)

randMat = 3x4
0.0733    0.5905    0.1731    0.1795
0.0550    0.8539    0.1340    0.3175
0.3232    0.2871    0.9947    0.5683

% 2. Maximum Value and Maximum Index
[maxVal maxIndex] = max(randMat)

maxVal = 1x4
0.3232    0.8539    0.9947    0.5683

maxIndex = 1x4
3     2     3     3

% 3. Linear index
linearIdx = maxIndex + ((1:stateCount)-1)*choiceCount

linearIdx = 1x4
3     5     9    12

% 4. Optimal Choices
randMat(linearIdx)

ans = 1x4
0.3232    0.8539    0.9947    0.5683