# Note on aggregating demand

## Public goods

Most economic goods are rival – if one person consumes something, no one else can.

Many environmental goods are non-rival, meaning if one person uses something, it doesn’t impact the consumption value for anyone else:

• clean air
• beautiful landscape

Non-rival goods commonly called public goods

Note:

• A second important of economic goods is whether or not they are excludable
• If a good is excludable, people can be prevented from using it.
• Non-rival non-excludable goods are called pure public goods
• Non-rival excludable goods are called club goods
• example: DirectTV

## Aggregate demand for a public good

• benefit estimation typically occurs at the micro level

• by for policy evaluation, we’re often interested in calculating total benefits
• area under the aggregate demand curve up to the point of the policy
• to do this, we need to aggregate the demand curves of all affected parties

### Adding demand curves: private goods

• normal private goods are rival
• example: an apple
• need to sum demand horizontally!
• demand typically takes the form of Q(P)
• however, supply and demand graphs presented as P(Q)
• need to invert demand first
• ie we want to add up all Q demanded at a given P, not sum over P at a common Q

### Steps:

– solve for $q_{i}(P)$

– sum up over all $i$ at the same $P$ to get $Q$

– now invert again to get $P(Q)$

### Example: Demand for apples

• two consumers, $A$ and $B$
• A really likes apples: $P=20-Q_{A}$
• B likes them less: $P=10-Q_{B}$

Graph these. What does total (aggregate) demand look like?

1. Solve for Q
$Q_{A}=20-P$
$Q_{B}=10-P$

2. Add curves if Q > 0
[Can’t have negative demand] $Q_{T}=20-P$ if $P > 10$ $Q_{T}=30-2P$ if $P \le 10$

3. Now invert back to graph: $P=20-Q_{T}$ if $Q < 10$
$P=15-Q_{T}/2$ if $Q \ge 10$

### Imagine the good is instead a very rare animal

– neither A nor B ever see it, but get utility from its existence

• Now Q is non rival (and non excludable)

– so $Q_{T}=Q_{A}=Q_{B}$

What does the aggregate demand curve look like now?

### Calculating demand for a pure public good

Assume same demand curves: • A gets utility up to the point where 20 are saved: $P=20-Q_{A}$

• B only cares as long as there are 10: $P=10-Q_{B}$

Now we actually do want to add vertically

$P=30-2Q$ if $Q \le 10$ $P=20-Q_{T}$ if $Q > 10$

### Summary on calculating total benefits

• To get the total consumer benefits of policy, we want the area under the demand curve.
• If they incur a private cost, subtract that.
• If the cost is public (for example paid for by the government), remove that from net benefits, but not consumer surplus
• Often times demand curves are estimated at the individual level
• To get the aggregate demand for a rival good, need to add horizontally.
• To get the aggregate demand curve for a non-rival good, need to sum vertically.

[this is useful for the problem set]