When disasters hit an area, the cost of everything--food, water, housing, gas and so forth--seems to go up immediately

The law of supply states that there is a positive relationship between the price and the quantity supplied of a good or service, keeping other factors affecting the supply constant.

When a disaster hit a region, the supplies of all the essentials like food, water, housing, gas, etc decreases because of no or very less transportation. The supply decreases.

With the demand being constant, the prices rise as to bring the market into equilibrium. Higher prices increases the profits of the firms and there is an urge in the firms to produce more output. This helps the economy to increase the level of income multiplier times.