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Exercises · Q10

Q.Using supply and demand curves, show how an increase in the price of shoes affects the price of a pair of socks and the number of pairs of socks bought and sold.

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Shoes and socks are complements — goods consumed together. When the price of shoes rises, demand for socks falls (leftward shift), lowering both the equilibrium price and quantity of socks traded.

The economic intuition: complements and cross-price effects

Shoes and socks are consumed jointly. You wear them together, so the demand for one depends on the consumption of the other. When the price of shoes increases, fewer people buy shoes — either they postpone the purchase, buy fewer pairs, or exit the market altogether. Because socks are useful primarily when you have shoes to wear them with, the demand for socks falls as well. This is the hallmark of complementary goods: a rise in the price of one reduces the demand for the other.

Notice that the supply curve of socks itself does not move. Sock manufacturers face the same costs, technology, and input prices as before. What changes is how many socks consumers want at each price, and that is captured by a shift in the demand curve.

What happens in the sock market

Start with the initial equilibrium in the market for socks, where the demand curve D0D_0 intersects the supply curve SS at price P0P_0 and quantity Q0Q_0.

When the price of shoes rises:

  • Demand for socks shifts left from D0D_0 to D1D_1. At every price level, consumers now wish to buy fewer pairs of socks because they are buying fewer shoes.
  • The supply curve SS remains unchanged.
  • The new equilibrium occurs at the intersection of D1D_1 and SS, yielding a lower price P1<P0P_1 < P_0 and a lower quantity Q1<Q0Q_1 < Q_0.
Watch out

A common mistake is to think the supply of socks shifts. It does not. The change in the price of shoes affects buyers' willingness to purchase socks, not producers' willingness to supply them. Only the demand curve moves. …

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