Econ Lab · Markets

Price controls

Coffee settles at four dollars a cup on its own. Now suppose a government decides that is too dear and caps the price at three. It sounds like a gift to buyers. Watch what actually happens to the number of cups that get made.

Slide the control price below the market level and then above it. The market answers in shortages and gluts.

024680100200300400
Cups of coffee\text{Cups of coffee}
Price per cup ($)\text{Price per cup (\$)}
DD
SS
deadweight loss\text{deadweight loss}
price ceiling\text{price ceiling}
shortage

A ceiling held below the market price means cafes brew only 150150 cups, because at 3.003.00 dollars a cup that is all they will make. Buyers want 250250, so a shortage of 100100 cups opens up. The pressure is upward, buyers would gladly pay more, but the price is capped and cannot rise to call out the extra cups. The shaded triangle is the deadweight loss: trades that helped both sides, gone because the price is not allowed to clear them.

Drag the slider. Below four dollars the cap bites and a shortage opens, above it a floor bites and a glut piles up. The shaded triangle is the surplus destroyed either way.

The short side wins

A price fixes one number, but buyers and sellers react to it differently. At any controlled price the quantity demanded and the quantity supplied are two separate numbers, and only the smaller of them actually trades. Nobody can be forced to buy or sell.

Qtraded=min(QD,  QS)Q_{\text{traded}} = \min\left(Q_D,\; Q_S\right)

Whoever is on the short side sets the volume. Under a cap that is the sellers, under a floor it is the buyers.

A ceiling makes a shortage

Hold the price below four dollars and cafes pull back. At three dollars they will brew only a hundred and fifty cups, yet buyers now want two hundred and fifty. The gap is a shortage. The cups exist in the demand, they just never get made, because the price is not allowed to rise far enough to coax them out.

A floor makes a glut

Push the price above four dollars and the picture flips. Cafes would love to sell more at the higher price, but buyers walk away, so unsold coffee piles up. This is what a minimum wage or a farm support price does in its own market: the side that has to buy at the propped-up price simply buys less.

The triangle nobody sees

The shaded wedge is the real cost. Between the controlled volume and the free-market two hundred cups sit trades where a buyer valued the coffee more than it cost a cafe to make. Both sides would have gained, and the control quietly erases them. That lost surplus is deadweight loss, and it is the reason a price control rarely helps as much as it promises.

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