Demand and Utility

1
Demand and Utility
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Diminishing Marginal Utility

• The more you have of a good, the less an
  additional unit of the good is worth to you.

3
Utility Maximization Condition

• The additional satisfaction obtained from
  purchasing another dollars worth of a good
  should be equal for all goods.

4
Example
apples
plums
price 0.25 MU 3
price 0.50 MU 4
How can you tell your utility isnt maximized?
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1 worth of apples
1 worth of plums
4 u

3 u
3 u
4 u
3 u
3 u
8 units of satisfaction
12 units of satisfaction
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If you spend 1 less on apples, you would lose 2
apples.

4 u
4 u
That would reduce your satisfaction by 8 units.
8
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If you spend 1 more on plums, you would gain 4
plums.

3 u
3 u
3 u
3 u
That would increase your satisfaction by 12 units.
12
8
So,
increase of 4 units of satisfaction.

8

12

• If before making the adjustment, your total
  utility was 20 units, your total utility after
  the adjustment would be 20 4 24.

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Once again In order to maximize utility, the
additional satisfaction from another dollars
worth of a good should be equal for all goods.

• In other words The marginal utility per
  dollar should be equal for all goods.
• MUa / Pa MUb / Pb

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Lets apply the formula MUa / Pa MUb /
Pbdirectly to our example.

• For apples, MU / P 4/.50
  8.For plums, MU / P 3/.25 12.
• Since 8 does not equal 12, utility was not
  maximized.

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As you eat fewer apples, the value to you of an
apple increases, perhaps from 4 to 5.

• As you eat more plums, the value to you of a
  plum decreases, perhaps from 3 to 2.5.
• Then for apples, MU / P 5/.50
  10.and for plums, MU / P 2.5/.25
  10.
• Now the marginal utilities per dollar are
  equal for the two goods and no adjustments will
  make you any happier.

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The Connection between Demand and Utility

• Instead of thinking in terms of utils, lets
  think in terms of dollars.
• Suppose the purchase of one unit of a good
  gives you 10 worth of satisfaction.
• In other words, the marginal utility of that
  first unit of the good is 10.
• Then you would be willing to pay up to 10 for
  it.

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• If a second unit of the good contributes 8
  more of satisfaction, the marginal utility of
  your second unit is 8 and you would be willing
  to pay up to 8 for it.
• If a third unit of the good contributes 6
  more of satisfaction, the marginal utility of
  your third unit is 6 and you would be willing to
  pay up to 6 for it.

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Remember that the demand curve tells you what
people are willing to pay for various amounts of
a good or, equivalently, how many units of a good
they are willing to purchase at various prices.

• So, since we just found that the marginal
  utility tells us what we are willing to pay for a
  good, the marginal utility provides us with
  information that we can use to determine our
  demand curve.

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In our example, we had the following
Number of units purchased (Q) Price you are willing to pay (P) Marginal Utility
0 - -
1 10 10
2 8 8
3 6 6
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If we graph that information, we get our demand
curve.
Number of units purchased (Q) Price you are willing to pay (P) Marginal Utility
0 - -
1 10 10
2 8 8
3 6 6
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Notice that by adding our MU values we can
determine our total utility at different
consumption levels.
Number of units purchased (Q) Price you are willing to pay (P) Marginal Utility Total Utility
0 - - 0
1 10 10 10
2 8 8 18
3 6 6 24
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Lets combine our new information with the ideas
we had earlier.

• Recall that we maximize our utility where the
  marginal utility per dollar is equal for all
  goods.

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In addition, we concluded that we increase our
purchases of a good as long as our marginal
utility is greater than the goods price.

• Recall marginal utility drops as we consume
  more and more of a good.
• So we would consume a good until we get to the
  point where our marginal utility is equal to its
  price.
• That is, MU P
• or MU/P 1.

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• So, we purchase up to the point where MU/P is
  equal for all goods and MU/P1 for each good.
• So to maximize our utility, we consume such
  that our marginal utility per dollar is equal for
  all goods, and we do that up to the point where
  we either run out of money or

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Consumer Surplus

• the difference between what you have to pay
  for a good and what you would have been willing
  to pay.

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Example

• Suppose that you would have been willing to
  pay 25 for a pair of jeans. When you get to the
  store, you find them selling for 20. What is
  your consumer surplus?
• consumer surplus 25 - 20 5

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• In terms of a supply and demand graph, the
  consumer surplus is the area under the demand
  curve and above the price.

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Graphing Consumer Surplus

• price

supply
demand
quantity
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Graphing Consumer Surplus

• price

supply
P
demand
quantity
Q
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Graphing Consumer Surplus

• price

supply
P
demand
quantity
Q
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Example Using the graph below, determine the
consumer surplus.

• Price
• 10

supply
consumer surplus (1/2)(base)(height) (1/2)
(8)(4) 16
P 6
demand
quantity
0 Q 8
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We can also calculate consumer surplus using the
information in our earlier utility table.
Number of units purchased (Q) Price you are willing to pay (P) Marginal Utility Total Utility
0 - - 0
1 10 10 10
2 8 8 18
3 6 6 24
Remember that consumer surplus is the difference
between what you are willing to pay for a good
(or what its worth to you) and what you have to
pay for it.
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Number of units purchased (Q) Price you are willing to pay (P) Marginal Utility Total Utility
0 - - 0
1 10 10 10
2 8 8 18
3 6 6 24
What the good is worth to you is its TU, which is
the sum of the MUs, or equivalently the sum of
the prices that you would be willing to pay for
each unit of a good. Suppose the price is 6.
You purchase three units of the good, and their
total worth to you is TU24. But since you only
have to pay 6x318, your consumer surplus would
be 24-186.