Today I have a hypothetical example to explain elasticity of demand.
A company, Cogco, manufactures cogs. Each cog contains two inputs: a widget and a sprocket. Cogco buys its sprockets for $99,000 each and its widgets for $1,000 each. It sells the cogs for $110,000 for a profit of $10,000 per cog (that's a 10% markup but a 9.1% profit margin).
Now imagine that the widget manufacturers get together and form a cartel. The cartel decides that no widget will be sold for less than $1,400, a 40% price increase. What happens to demand for widgets? There is probably no change in demand at all, because even at $1,400 per widget, Cogco has a $9,600 profit per cog. Cogco's manufacturing costs have only increased by 0.4% as a result of the 40% increase in the cost of widgets.
We can say that widgets have a perfectly inelastic demand curve between $1,000 and $1,400.
The sprocket manufacturers see the success of the widget cartel, so they decide to do the same thing. They also raise their price by 40%, from $99,000 to $138,600. What happens to the demand for sprockets? Well this depends on the elasticity of demand for cogs, because Cogco will have to raise its prices. $140,000 is now the lowest price that Cogco can charge and not lose any money. It's possible that there's a good substitute for cogs which sells for $130,000, and in that case sales of cogs could fall to near zero because all the customers will buy the less expensive substitute.
This example demonstrates the principle that low priced goods have low elasticities of demand. This is why the price of gasoline doubled yet there was no decrease in demand. The price of gasoline is low compared to the much higher price of the motor vehicle it powers. On the other hand, if the price of cars doubled, I'm sure you'd see a decrease in the number purchased.
What does this have to do with the minimum wage? The minimum wage worker is like the widget in the example above. About 3% of workers earn the minimum wage, and that wage is about 25% of the average wage, so minimum wage workers represent less than 1% of the economy's labor inputs. Therefore, it's unlikely that a 40% increase in the cost of a minimum wage worker would have much effect on demand for their labor. Nor would it have much effect on prices of goods either. Overall prices might increase by 0.4% as a result of the minimum wage increase, an amount much smaller than the normal annual rate of inflation, so the price increase would hardly be noticed.
Why have I written this post? To counter the nonsense examples of people like the GMU professors who run the Cafe Hayek blog. They are constantly predicting massive unemployment or runaway inflation as a result of a 40% increase in the minimum wage.