ch05 - Chapter 5 The Theory of Demand 1 The price...

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1 Chapter 5:  The Theory of Demand Chapter 5:  The Theory of Demand
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2 The       is the set  of optimal baskets for every possible price of good x,  holding all other prices and income constant. price consumption curve   of good x
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3 Y (units) X (units) 0 P X = 4 X A =2 X B =10 10 P Y = $4 I = $40 Example:   The Price Consumption Curve
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4 Y (units) X (units) 0 P X = 4 P X = 2 X A =2 X B =10 10 P Y = $4 I = $40 20 Example:   The Price Consumption Curve
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5 Y (units) X (units) 0 P X = 4 P X = 2 P X = 1 X A =2 X B =10 X C =16 10 P Y = $4 I = $40 Price consumption curve 20 The price consumption curve for good x  can be written as the quantity consumed of  good x for any price of x.  This is the  individual’s demand curve for good x. Example:   The Price Consumption Curve
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6 Example:   Individual Demand Curve for X X P X X A X B X C Individual Demand Curve For X P X = 4 P X = 2 P X = 1 U increasing
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7 The consumer is maximizing utility at every point  along the demand curve The marginal rate of substitution falls along the  demand curve as the price of x falls (if there was an  interior solution). As the price of x falls, utility increases along the  demand curve.
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8 Example:  Suppose U = x + y.  Income, I, is spent  only on x and y.  Prices are p   x  and p   y . When p x  < p y , the price consumption curve is  I/p x = x.   When p x  > p y , the price consumption curve is I/p y  = y*.   Between, it is x + y = I
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9 Example:   The Price Consumption Curve X (units) Y*=I/P Y P X >P Y 0 Y (units)
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10 10 Example:   The Price Consumption Curve X (units) Y*=I/P Y P X >P Y P X =P Y P X <P Y 0 Y (units)
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11 11 Example:   The Price Consumption Curve X (units) Y*=I/P Y P X >P Y P X =P Y P X <P Y IC 1 IC 2 IC 3 0 Y (units)
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12 12 The corresponding demand  for x is:    X = I/p x    when p x  < p y          I – y when p x  = p y  when p x  > p y X P X 0 P Y I/P Y -Y I/P X Demand curve for X
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13 13 Algebraically, we can solve for the individual’s demand  using the following equations: 1.  p x x + p y y = I 2.  MU x /p x  = MU y /p y  … at a tangency. (If this never holds, a corner point may be substituted  where x = 0 or y = 0)
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14 14 Example: Finding a Demand Curve with an Interior Solution Suppose that U(x,y) = xy.  MU x  = y and MU y  = x. The prices  of x and y are p x  and p y , respectively and income = I. We have: 1.  p x x + p y y = I               2.  x/p y  = y/p x Substituting the second condition into the     budget  constraint, we have:  p x x + p y (p x /p y )x = I    or…x = I/2p x
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15 15 Suppose U = xy + 10x.  MU x =y + 10 and MU y  = x.  All the  other notation is as in the last example.
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