verification on a tricky basic economic problem

Quick verification question: Given that the hamburger market is regulated. If there are standard price government policy put forth to control the hamburger market, that is every hamburger must be sold for 3 dollars while the free market price of hamburger is 4 dollars. What will happen to the supply and demand curve if gov regulation is implemented and briefly describe whether or not hamburger shortage happened.

My work is: Both curve does not shift as the price only change the quantity demanded and quantity supply. Shortage will happen as the quantity demanded under the price ceiling is greater than the quantity of supply under the price ceiling

It's called price ceiling.
you can draw a standard demand and supply diagram, the y-axis is price and x-axis is quantity. and intersection of demand curve and supply curve is the equilibrium price $4.when there is a price ceiling at p=$3 (draw a horizontal line y=3), then you can get two points of intersection, the one with the demand curve, and the other with supply curve. you will find at this price (p=$3), the demand is larger than supply.

Your answer is correct. When a price ceiling is set in place, supply and demand curve does not change, the price ceiling creates a shortage where the vendors will not produce as much at the lower price while consumers will demand more because the hamburgers are cheaper.

Since there is a price ceiling, the free market price of 4 dollars simply does not exist. In other words, the ceiling is set below the equilibrium point. Sellers would be discouraged to sell, but buyers will have intend to buy. However, the supply and demand curves do not move at all. It's simply an action of the price ceiling.