Consumer Choices

Some useful links to understand the Lagrange multiplier:

  • An introductive article here
  • On the interpretation of the Lagrange multiplier here and here

For all notation, please use the one from the image on the left. The rule is: uppercase for functions, lowercase for variables and parameters.



Slutsky equation:

  • A useful video here
  • An intuitive approach to the Slutsky equation here

Compensating and equivalent variations:

  • The compensating variation is like asking yourself : “How much must I compensate you to make you as well off as you were before the price change?

In Ex 5e) The consumer needs 50 units of income to accept the economic change (i.e. price change)

  • The equivalent variation is, at the initial prices, what is the amount of income necessary to get to the new level of utility?

In Ex 5e) 100/3 units of income is the amount that would be taken away to lower the consumer's utility to the level that would happen if the change had occur (i.e. u1)

  • A useful video here on CV and EV

What you should know at the end of this chapter:

  • Master the primal and the dual consumer program
  • Use the Lagrangien to optimize a function subject to a constraint
  • Compute the Marshallian and Hicksian demand function
  • Define and determine the indirect utility function and the expenditure function
  • Know the 4 fundamental identities
  • Know the Shepard's lemma, Roy's identity and the Slutsky equation
  • Differentiate the substitution and the income effect of the price variation (mathematically and graphically)
  • Compute and understand the compensating and the equivalent variation
  • Know how to demonstrate that a function is homogeneous of degree k and interpret the results