Demand

Intermediate Microeconomics (Econ 100A)

Kristian López Vargas

UCSC - Spring 2017

Demand function

  • "Optimal bundle" for generic prices and income = Demand Function.

  • The "optimal bundle" changes when income or prices change: that is why we call it demand function.

Demand function

  • For a specific utility (preferences) and given set of income and prices, we have learned how to find the optimal bundle.

  • If you solve this, so called, consumer's problem for generic income and prices $ (p_1,p_2,m) $, what you obtain is the demand function: $ x_1^{*}(p_1,p_2,m) $.

  • For example, if utility is Cobb-Douglas, then $ x_1^{*} (p_1,p_2,m) = \frac{a m}{ (a+b) p_1} $

A consumer's demand function indicates the optimal choice for a given set of prices and income.

Changes in income

$ x_1 = x_1(p_1,p_2,m) $

  • How does the optimal consumption of $ x_1 $ changes with changes in income? $ \frac{\partial x_1}{ \partial m } $ Vs. $ 0 $

  • A normal good: its consumption increases when income increases.
    • $ \frac{\partial x_1}{ \partial m } > 0 $
    • Do graph
  • An inferior good: its consumption decreases when income increases.
    • $ \frac{\partial x_1}{ \partial m } < 0 $
    • Do graph

Engel Curve

  • The Engel Curve maps each level of income to the optimal consumption of a good, holding prices constant.

Engel Curve - Inferior good

Changes in prices

  • $ \Delta p_1 $ tilts or pivots the budget line.

  • How does the optimal consumption of $ x_1 $ changes with changes in $ p_1 $? $ \frac{\partial x_1}{ \partial p_1 } $ Vs. $ 0 $

  • Ordinary good: its consumption decreases when its price increases.
    • $ \frac{\partial x_1}{\partial p_1} < 0 $
    • Do graph
  • Giffen good: its consumption increases when its price increases.
    • $ \frac{\partial x_1}{\partial p_1} > 0 $
    • Do graph

Demand curve

  • Demand curve: describes the relationship between the optimal choice of a good and its price, with income and other prices held constant.

Giffen Good

Substitutes and Complements

  • Gross Substitutes: $ \frac{\partial x_1}{ \partial p_2 } > 0 $

  • Gross Complements: $ \frac{\partial x_1}{ \partial p_2 } < 0 $