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[harrison_creps] Use linear solver instead of matrix inverse #669

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[harrison_creps] Use linear solver instead of matrix inverse #669

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11 changes: 7 additions & 4 deletions lectures/harrison_kreps.md
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Original file line number Diff line number Diff line change
Expand Up @@ -276,11 +276,14 @@ def price_single_beliefs(transition, dividend_payoff, β=.75):
"""
Function to Solve Single Beliefs
"""
# First compute inverse piece
imbq_inv = la.inv(np.eye(transition.shape[0]) - β * transition)
# First compute (I - βQ)
A = np.eye(transition.shape[0]) - β * transition

# Next compute prices
prices = β * imbq_inv @ transition @ dividend_payoff
# Next compute βQd
b = β * (transition @ dividend_payoff)

# Solve linear system
prices = la.solve(A, b)

return prices
```
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