It's basic microeconomics. Firms produce widgets until the marginal profit they get from the widgets goes down to 0. The marginal profit is based on the marginal cost of producing a widget and the current price of the widget. If the price goes up, the firm can now afford to produce more widgets. If the state introduces price controls to keep the price fixed during increased demand, the company cannot afford to produce more to meet this demand and shortages will result.
Normally shortages lead to increased price in the short term and in the long term lead to increased production and movement to the price equilibrium.
Sorry, but how exactly does that follow?