I don't believe that this cupcake market example proces that payday loans introduces a negative externality. An externality only occurs if cupcakes introduced

I don't believe that this cupcake market example proces that payday loans introduces a negative externality. An externality only occurs if cupcakes introduced a harm or benefit to third parties that was not factored into the cupcake price. For instance, cupcakes might cause pollution (e.g. discarded cupcake wrappers) which would cause a negative externality because there's no "cupcake tax" to fund pollution cleanup. Conversely, cupcakes might cause an increase in the number of happy people in the world, which would be a positive externality. To successfully conclude that payday loans introduce a negative externality, we need to point to a specific harm to third parties beyond higher or lower prices. For instance, one might assert that payday loan customers who rely on payday loans are more likely to resort to drug use or crime, which then harms society. However, that isn't the argument presented here. Also, in your other examples, there are repeated mentions to a fixed supply ("a limited number of houses", "a limited number of spots in colleges", "a limited amount of food".) Economic theory would suggest that higher prices would result in higher supply. For instance, when the price of cupcakes go up from $2, bakers will respond by producing more cupcakes and the supply of cupcakes will increase. This will lower the price of cupcakes from $10 to (say) $3. Granted, $3 is higher than $2, but that's just the market equilibrium price when payday-loan users are allowed to have inter-temporal credit.