Equilibrium in the apple market and a statutory minimum price of ₹75

Equilibrium without the law. The equilibrium price is the one at which quantity demanded equals quantity supplied:

176 – 2P = –16 + P, so 192 = 3P and P = ₹64.

Then Qd = 176 – 2 × 64 = 48 and Qs = –16 + 64 = 48, so the equilibrium quantity is 48 apples (in the units of the question).

The minimum price binds. A statutory minimum price is a price floor: a lower limit, set by the government, on the price that may be charged. A floor matters only when it is set above the equilibrium price, and then it creates an excess supply. Here ₹75 is above ₹64, so the floor binds and the market price rises to ₹75. At that price:

• quantity demanded = 176 – 2 × 75 = 26;
• quantity supplied = –16 + 75 = 59;
• the excess supply (surplus) is 59 – 26 = 33.

Buyers cannot be made to buy more than they want, so only 26 apples are actually bought and sold, 22 fewer than before.

Surpluses before the law. Consumer surplus is the area below the demand curve and above the price; producer surplus is the area above the supply curve and below the price. The demand curve meets the price axis at ₹88 (where Qd = 0) and the supply curve at ₹16 (where Qs = 0).

• Consumer surplus = ½ × 48 × (88 – 64) = ₹576.
• Producer surplus = ½ × 48 × (64 – 16) = ₹1,152.
• Total surplus = 576 + 1,152 = ₹1,728.

Surpluses after the law. We take the 26 apples sold to come from the sellers with the lowest costs, those lowest on the supply curve. The supply price of the 26th apple is 16 + 26 = ₹42.

• Consumer surplus = ½ × 26 × (88 – 75) = ₹169.
• Producer surplus = (75 – 42) × 26 + ½ × 26 × (42 – 16) = 858 + 338 = ₹1,196.
• Total surplus = 169 + 1,196 = ₹1,365.

The fall in total surplus, 1,728 – 1,365 = ₹363, is the deadweight loss: the 22 apples between 26 and 48 were each worth more to a buyer than they cost a seller to grow, and they are no longer traded, so their gain goes to no one. As with a tax, the lost trades are the market's inefficiency. It equals the triangle ½ × 22 × (75 – 42) = ½ × 22 × 33 = 363.

Summary of the changes.

Buyers lose on two counts: they pay more for each apple and buy fewer. Sellers who still sell gain from the higher price more than they lose on the smaller quantity, so producer surplus rises a little, but less than consumers lose.

The other reading. The question does not say what happens to the 33 unsold apples. If, as in agricultural price support, the government buys the surplus at the minimum price, sellers sell all 59 apples at ₹75 and producer surplus becomes ½ × 59 × (75 – 16) = ₹1,740.50; consumer surplus is still ₹169, and the government pays 75 × 33 = ₹2,475 for apples nobody in the market wanted. On our main reading no one buys the surplus.