Rephrasing

app.py

@@ -38,7 +38,7 @@ utilities (e.g., Tampa Electric) as it allows to **adjust prices to changes in d
 st.markdown("""It is hardly surprising that recent times of extraordinary uncertainty and volatility
 caused a surge in adoption of dynamic pricing strategies with an [estimated 21% of e-commerce 
 businesses reportedly already using dynamic pricing](https://www.statista.com/statistics/1174557/dynamic-pricing-ecommerce-companies-worldwide/) 
-and an additional 15% planning to adopt thestrategy in the upcoming year.""")
+and an additional 15% planning to adopt the strategy in the upcoming year.""")
 st.markdown("""To find a big success story, we should look no further than Amazon who (on average)
 change their products' prices once every 10 minutes. They attribute roughly [25% of their e-commerce
 profits](https://dzone.com/articles/big-data-analytics-delivering-business-value-at-am)
@@ -72,6 +72,9 @@ st.markdown("""Now that we have a reasonable estimate of our demand function, we
 expected profit at different price points because we know the following holds:""")
 st.latex(f"{profit} = {p}*{sympy.Function(D)(p)} - [{var_cost}*{sympy.Function(D)(p)} + {fixed_cost}]")
 st.image("assets/images/ideal_case_profit_curve.png")
+st.markdown("""Note that fixed costs (e.g., rent, insurance, etc.), per definition, don't vary when
+demand or price changes. Therefore, fixed costs have no influence on the behavior of dynamic pricing
+algorithms.""")
 st.markdown("""Finally we can dust off our good old high-school math book and find the
 price which we expect will optimize profit which was ultimately the goal of all this.""")
 st.image("assets/images/ideal_case_optimal_profit.png")
@@ -176,9 +179,11 @@ st.markdown("This results in the following expected profit curve")
 st.image("assets/images/posterior_profit_sample.png")
 st.markdown("""And eventually we arrive at a new price: €5.25! Which is indeed considerably closer
 to the actual optimal price of €4.24""")
-st.markdown("""Now that we have our first updated price point, why stop there? Let's simulate 10 
-demand data points at this price point from out latent demand curve and check whether Thompson 
-sampling will edge us even closer to that optimal €4.24 point.""")
+st.markdown("Now that we have our first updated price point, why stop there?")
+st.markdown("""With \"pure\" Thompson sampling, we would sample a new demand curve (and thus price
+point) out of the posterior distribution every time. But since we are mainly interested in seeing
+the convergence behavior of Thompson sampling, let's simulate 10 demand points at this fixed €5.25
+price point.""")
 st.image("assets/images/updated_prices_demand.png")
 st.markdown("""We know the drill by now.  \n
 Let's recalculate our posteriors with this extra information.""")