From deca89687f580ba880b7df9d734bc4bc4b7ffb6e Mon Sep 17 00:00:00 2001
From: UdohNakamura <159118172+UdohNakamura@users.noreply.github.com>
Date: Mon, 3 Nov 2025 13:55:32 +0900
Subject: [PATCH] Refactor price_single_beliefs function

Refactor price_single_beliefs function to improve clarity and efficiency.
---
 lectures/harrison_kreps.md | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/lectures/harrison_kreps.md b/lectures/harrison_kreps.md
index 03cc6d269..1c91158af 100644
--- a/lectures/harrison_kreps.md
+++ b/lectures/harrison_kreps.md
@@ -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
 ```