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1 Market Demand from Individual Demand

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2 In this section we want to think about market demand as the result of adding up demands from many individuals. Remember individual demand is the result of each consumer going about utility maximization. Lets do an example with 3 people. qi is the demand from the ith consumer. Say, q1 = 10 - p, q2 = 15 - 2p, andq3 = 18-3p. Often the demand is written in inverse form (where we isolate the p term). We have p = 10 - q1,p = 15/2 - (1/2)q2, and p = 18/3 - (1/3)q3 We usually express demand in inverse form when we want to graph the demands in the P, Q graph. I have a graph on the next screen with each demand in it.

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3 P Q 10 7.5 6 101518 Note at a price above 10 no one demands any units. At a price above 7.5 only person 1 demands units. At a price above 6 only person 1 and person 2 demand units. If price is below 6 all three people demand units. The dashed line here is the market demand. It is found by looking at each price and adding the quantities each person would demand.

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4 To get the market demand we horizontally add the demand from each person. This amounts to saying q1 + q2 + q3 = Q. We saw before the demand from each person was q1 = 10 - p, q2 = 15 - 2p, andq3 = 18-3p. To get the market demand we add q1 + q2 + q3 to get (10 - p) + (15 - 2p) + (18 -3p) = (10 + 15 + 18) - (p + 2p + 3P), or Q = 43 - 6P, but this is only true when price is less than or equal to 6. In other words all three people demand units when the price is less than 6. Note if P = 1 q1 = 9, q2 = 13, q3 = 15 and Q = 37, or if P = 2 q1 = 8, q2 = 11, q3 = 12 and Q = 31.

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5 P Remember if the price is above 6 but less than or equal to 7.5 the demand comes from only the first two people and the demand curve is q1 + q2 = Q = 25 - 39, and if the price is above 7.5 the demand is only from the first person and the demand curve is q1 = Q = 10 - p. So the market demand curve we have come to know and work with is really the addition of the demand from many people as they have gone about maximizing their utility. Q

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