week4 Handout (6pp)

week4 Handout (6pp) - Consumers Surplus A consumers demand...

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1 Consumer Surplus Chapter 14 Consumer’s Surplus A consumer’s demand curve for a good (say good 1) tells us that, at any given price p 1 , the consumer is willing to buy some determinate quantity x 1 of the good. When the consumer does so, he is presumably better off than he was when he had no units of good 1, and had not paid any money for it. ―Consumer’s surplus‖ is a measure of the increase in well-being that occurs because the consumer is able to buy a good on the market. 2 Consumer’s Surplus Think of the two goods as good 1 and ―all other goods‖, where the latter is measured in units of $1. The consumer starts with $m of income and no good 1. Thus his utility is U(0, m). If he buys x 1 units of good 1 at price p 1 , then he will have m-p 1 x 1 to spend on other goods, so his utility will be U(x 1 , m-p 1 x 1 ). The net consumer’s surplus he gains from participating in the market for x 1 is then U(x 1 , m-p 1 x 1 ) U(0, m) Which should be positive, otherwise he has not behaved optimally in buying good 1. 3 Reservation price To measure consumer’s surplus, we use the concept of reservation price . This is an idea that is useful in other contexts as well. The consumer’s reservation price of the next unit is the amount of money that he is willing to pay for one more unit of that good. The reservation price is a dollar measure of the utility gain that the consumer gets from another unit of the good. 4 Suppose petrol can be bought only in lumps of one litre. Use r 1 to denote the most a single consumer would pay for a 1st litre -- this is her reservation price for the 1st litre. r 1 is the dollar equivalent of the marginal utility of the 1st litre. Now that she has one litre, use r 2 to denote the most she would pay for a 2nd litre -- this is her reservation price for the 2nd litre. $-equivalent Utility Gains: example 5 If she already has n-1 litres of petrol then r n denotes the most she will pay for an nth litre. r n is the dollar equivalent of the marginal utility of the nth litre. r 1 + … + r n will therefore be the dollar equivalent of the total change to utility from acquiring n litres of petrol at a price of $0. A plot of r 1 , r 2 , … , r n , … against n is a reservation-price curve. This is similar, but not quite the same as the consumer’s demand curve for petrol. $-equivalent Utility Gains: example 6
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2 Let p G be the price the consumer pays for petrol. price is in $ per litre. So [r 1 + … + r n ] - p G n will be the dollar equivalent of the total change to utility from acquiring n litres of petrol at a price of $p G each.
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week4 Handout (6pp) - Consumers Surplus A consumers demand...

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