## C The collective optimum for collective goods

To obtain the collective optimum for collective goods, we must not add together the individual demands of consumers, because they do not all need to have their own collective goods (their own road bridges or parks). Instead, we can only usefully add up the willingness of A and B respectively to pay a particular price for these collective goods, which they can use jointly. For instance, A is prepared to pay A1 + A2 + ... + An = ATotai tax a week for bridges and B is prepared to pay B1 + B2 +... + Bn = BTotai. These two demand curves are presented in Figure B.4.

Bi the price A is prepared to pay per item

P the actual price per item

Cb costs A has to pay

BDb A's demand curve

BCbQbO A's marginal benefits

PCbQbO A's marginal costs

BCbP A's consumer surplus

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Qb Db

Quantity

Figure B.2 B's individual optimum for individual goods

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Quantity

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Quantity

Figure B.3 A and B's collective optimum for individual goods

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Qa Da Qb Db

Quantity Quantity

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Qa Da Qb Db

Quantity Quantity

Figure B.4 Demand curves for A and B for collective goods

Adding these demand curves vertically, as in Figure B.5, produces the total demand for bridges: Da+b. If, say, the actual price per bridge is P (P = Pa + Pb) tax a week, the optimum is at C: 6 bridges. At this point the maximum price that A and B are prepared to pay together for bridge 6 is the same as the actual price of a bridge. More bridges than 6 would represent a deterioration. Note that the maximum that A is prepared to pay for the first bridge is less than the actual price of a bridge, so A is unwilling and unable to pay for a bridge alone.

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