> The alternative is to have shortages.

This is a myth. The volume of inventory remains the same regardless of the price. When demand is higher than supply you have shortages regardless of price simply because you have unmet demand. If you raise prices, that demand is still unmet, you're now filtering that demand by who is willing to pay more so you maximize your own value and profit. Not even rationing prevents shortages because, again, the demand exists. Rationing simply tries to spread the supply around so more people get some rather than none. Price hikes instead say "who wants it badly enough?"