Final answer:
The monopolist with inelastic demand is more likely to be regulated due to potential higher profits and price gouging, while the same monopolist would also place a heavier burden on the government's budget if the product is made into a public good.
Step-by-step explanation:
When considering which of two natural monopolists with identical long-run average costs and horizontal long-run marginal costs is the less likely target for government regulation, we look at the demand elasticity for each product. With inelastic demand, the first monopolist can raise prices without causing a significant decrease in quantity demanded. This means the monopolist can maintain higher profits, thus drawing more scrutiny from regulators interested in protecting consumers from price gouging. Conversely, the second monopolist, facing elastic demand, cannot raise prices without significantly decreasing quantity demanded, which keeps prices closer to marginal costs and is less likely to prompt government intervention.
If the government considers making both products a 'public good,' the burden on the government's budget would primarily depend on the cost to produce the optimum quantity and the revenue needed to cover these costs. The product with inelastic demand would impose a heavier burden on the government's budget because the government would need to subsidize the monopolist to produce the socially optimal quantity at a price that is less than the average cost, leading to financial losses without subsidies.