1 / 31

The budget constraint and choice

The budget constraint and choice. The problem of limited resources and its effect on choice. The budget constraint and choice. Last week: We saw that preferences can be represented by utility functions ... That indifference curves can be used to map a utility function into “consumption space”

glevin
Download Presentation

The budget constraint and choice

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The budget constraint and choice The problem of limited resources and its effect on choice

  2. The budget constraint and choice • Last week: • We saw that preferences can be represented by utility functions ... • That indifference curves can be used to map a utility function into “consumption space” • But we still don’t know how consumers choose amongst the different bundles... • This week: • We introduce the concept of a budget, • This is the 2nd half of consumer theory

  3. The budget constraint and choice The budget constraint The optimal consumer choice Income and substitution effects

  4. The budget constraint • The basic concept is really straightforward: • The consumer has a limited income (I) to purchase different goods • Each type of good has a defined price (p) per unit • We assume that the consumer does not save and spends all his income • This possibility will be examined later

  5. The budget constraint • The general budget constraint for n goods is: • If we only look at 2 goods (Same simplification as last week), it can be expressed as:

  6. The budget constraint • Imagine the following “student entertainment budget” • You have 50 € • The price of a meal is 10 € • The price of a cinema ticket is 5 € • Your budget constraint is:

  7. Meals Maximum amount of meals you can buy  Cinema The budget constraint Diagram in “consumption space”

  8. Maximum amount of cinema tickets you can buy  The budget constraint Meals  Cinema

  9. The budget constraint Meals  Budget constraint  Cinema

  10. The budget constraint The budget constraint is Dividing by p1 and rearranging: Meals intercept  slope  Cinema

  11. H E C G F D The budget constraint Any bundle within the budget constraint is affordable , but not all the budget is spent (C,D). Meals  Any bundle beyond the budget constraint cannot be afforded (H,G). Any bundle on the budget constraint is affordable and ensures all the budget is spent (E,F).  Cinema

  12. The budget constraint Meals Budget set  Budget constraint  Cinema

  13. The budget constraint • The position of the budget constraint depends on • The income of the agent (I) • The price of the two goods (p1 and p2)

  14. The budget constraint Effect of a fall in income (I) Meals   Cinema

  15. The budget constraint Increase in the price of cinema tickets Meals   Cinema

  16. The budget constraint and choice The budget constraint The optimal consumer choice Income and substitution effects

  17. The optimal consumer choice • This requires bringing in the two elements of the theory • The indifference curves, which show how agents rank the different bundles • The budget constraint, which shows which bundles are affordable, and which are not • Both of these are defined over the “consumption space”, so they can be superposed easily

  18. Optimal bundle F  The optimal consumer choice Which is the best bundle ? Meals  A C   B D   E   Cinema

  19. Definition of the MRS at F !!!  The optimal consumer choice The budget constraint is tangent to the indifference curve at F Meals  F  Cinema

  20. The optimal consumer choice • The optimal bundle is on the tangency between the budget constraint and the indifference curve. • This means that for the optimal bundle the slope of the indifference curve is equal to the slope of the budget constraint MRS = ratio of prices

  21. The optimal consumer choice • This condition gives a central result of consumer theory: • The optimal bundle is the one which equalises the marginal utility per € spent • If you were to receive an extra € of income, your marginal utility will be the same regardless of where you spend it

  22. The optimal consumer choice Example of optimal choice with concave preferences The optimal solution is a “corner solution” Meals  F  G   Cinema

  23. The budget constraint and choice The budget constraint The optimal consumer choice Income and substitution effects

  24. Income and substitution effects • Consumer theory is used to understand how choice is affected by changes in the environment • These can be complex, and the theory helps to isolate these different effects • The separation of income and substitution effects is a good illustration of the concept of “ceteris paribus” • Each variable is isolated and analysed separately from the others

  25. Income and substitution effects An increase in the price of cinema tickets has 2 effects : • 1: A change in real income • A previously affordable bundle (A) is no longer affordable • 2: A relative price change • The slope of the budget constraint changes, and meals become relativelycheaper Meals  A   Cinema

  26. Income and substitution effects Effect of an increase in the price of cinema tickets on consumer choice • Fall in the consumption of cinema • Increase in the consumption of meals • Question: How can we separate the effect of the change in real income from the effect of the change in relative prices ? Meals   A B   Cinema

  27. Income and substitution effects In order to separate the 2 effects, we add animaginarybudget constraint • Parallel to the new budget constraint • Tangent to the original IC • There is only a single curve that satisfies these two requirements • This gives an imaginary optimal bundle (Im) Meals  Im   A B   Cinema

  28. Income and substitution effects The substitution effect • From A to Im, real income is held constant • We are still on the same indifference curve, so utility is the same • The change of bundle is due entirely to the change in relative price • This is the substitution effect Meals  Im   A B   Cinema

  29. Income and substitution effects The income effect • From Im, to B, relative prices are held constant • The two budget constraints are parallel, so the slope is the same • The change of bundle is due entirely to the fall in income. • This is the income effect Meals  Im   A B   Cinema

  30. Income and substitution effects The overall effect • By combining the two, one gets the overall effect • One can see that the interaction is different for the two goods • The 2 effects can work against each other, or add up • Depending on the relative strength of the effects, this can lead to increases or falls in consumption Meals  Im   A B   Cinema

  31. Income and substitution effects • This type of approach is fundamental to micro-economic analysis • Anyprice change is always accompanied by income and substitution effects. • So this helps understand the effects of taxation, shocks to prices, taste changes, etc. • Look at the complex effects of oil price increases on consumption • Price change ⇒ Complex change in bundle • Clearly, this will also help understand how demand curves are built (next week)

More Related