The Budget Constraint and Limited Resources

The concept of the budget constraint and its impact on choice due to limited resources. Understand how consumers with limited income make decisions on purchasing goods based on defined prices. Dive into examples and diagrams illustrating budget constraints in a consumption spaceT

• Budget constraint
• Limited resources
• Consumer choice
• Price
• Consumption

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Uploaded on Mar 07, 2025 | 0 Views

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1. THE BUDGET CONSTRAINT AND CHOICE THE PROBLEM OF LIMITED RESOURCES AND ITS EFFECT ON CHOICE

2. 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

3. THE BUDGET CONSTRAINT THE GENERAL BUDGET CONSTRAINT FOR N GOODS IS: = n I p x i i i 1 = IF WE ONLY LOOK AT 2 GOODS (SAME SIMPLIFICATION AS LAST WEEK), IT CAN BE EXPRESSED AS: = + I p x p x 1 1 2 2

4. 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: I = + p x p x 1 1 2 2 5 tickets 10 meals = + 50

5. THE BUDGET CONSTRAINT Diagram in consumption space Meals max meal x I Maximum amount of meals you can buy = max meal x p meal Cinema

6. THE BUDGET CONSTRAINT Meals max meal x Maximum amount of cinema tickets you can buy I = max cin. x p cin. max cin. x Cinema

7. THE BUDGET CONSTRAINT Meals max meal x Budget constraint max cin. x Cinema

8. THE BUDGET CONSTRAINT The budget constraint is Dividing by p1 and rearranging: = + I p x p x 1 1 2 2 Meals max meal x p p I = intercept x x 2 1 2 p 1 1 slope p p I = x x cin. meal cin. p meal meal max cin. x Cinema

9. THE BUDGET CONSTRAINT Any bundle within the budget constraint is affordable , but not all the budget is spent (C,D). Meals max meal x H Any bundle beyond the budget constraint cannot be afforded (H,G). E G C Any bundle on the budget constraint is affordable and ensures all the budget is spent (E,F). F D max cin. x Cinema

10. THE BUDGET CONSTRAINT Meals max meal x Budget set Budget constraint max cin. x Cinema

11. THE BUDGET CONSTRAINT THE POSITION OF THE BUDGET CONSTRAINT DEPENDS ON x = p p I x 2 1 2 p 1 1 THE INCOME OF THE AGENT (I) THE PRICE OF THE TWO GOODS (P1 AND P2)

12. THE BUDGET CONSTRAINT Effect of a fall in income (I) Meals max meal x max cin. x Cinema

13. THE BUDGET CONSTRAINT Increase in the price of cinema tickets Meals max meal x max cin. x Cinema

14. THE BUDGET CONSTRAINT AND CHOICE The budget constraint The optimal consumer choice Income and substitution effects

15. 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

16. THE OPTIMAL CONSUMER CHOICE Which is the best bundle ? Meals max meal x Optimal bundle A C B D F E max cin. x Cinema

17. THE OPTIMAL CONSUMER CHOICE The budget constraint is tangent to the indifference curve at F Meals max meal x Definition of the MRS at F !!! F max cin. x Cinema

18. 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 IC IS EQUAL TO THE SLOPE OF THE BUDGET CONSTRAINT MRS = RATIO OF PRICES

19. THE OPTIMAL CONSUMER CHOICE THIS CONDITION GIVES A CENTRAL RESULT OF CONSUMER THEORY: mU p MRS mU p mU p mU p = = = 2 2 1 2 1 1 1 2 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

20. THE OPTIMAL CONSUMER CHOICE Example of optimal choice with concave preferences The optimal solution is a corner solution Meals max meal x F G max cin. x Cinema

21. THE BUDGET CONSTRAINT AND CHOICE The budget constraint The optimal consumer choice Income and substitution effects

22. 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

23. 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 Meals max meal x 2: A RELATIVE PRICE CHANGE THE SLOPE OF THE BUDGET CONSTRAINT CHANGES, AND MEALS BECOME RELATIVELYCHEAPER A max cin. x Cinema

24. INCOME AND SUBSTITUTION EFFECTS Effect of an increase in the price of cinema tickets on consumer choice FALL IN THE CONSUMPTION OF CINEMA Meals max meal x 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 ? A B max cin. x Cinema

25. INCOME AND SUBSTITUTION EFFECTS In order to separate the 2 effects, we add an imaginary budget constraint PARALLEL TO THE NEW BUDGET CONSTRAINT Meals max meal x TANGENT TO THE ORIGINAL IC THERE IS ONLY A SINGLE CURVE THAT SATISFIES THESE TWO REQUIREMENTS Im THIS GIVES AN IMAGINARY OPTIMAL BUNDLE (IM) A B max cin. x Cinema

26. INCOME AND SUBSTITUTION EFFECTS The substitution effect FROM A TO IM, REAL INCOME IS HELD CONSTANT Meals max meal x WE ARE STILL ON THE SAME INDIFFERENCE CURVE, SO UTILITY IS THE SAME Im THE CHANGE OF BUNDLE IS DUE ENTIRELY TO THE CHANGE IN RELATIVE PRICE A B THIS IS THE SUBSTITUTION EFFECT max cin. x Cinema

27. INCOME AND SUBSTITUTION EFFECTS The income effect FROM IM, TO B, RELATIVE PRICES ARE HELD CONSTANT Meals max meal x THE TWO BUDGET CONSTRAINTS ARE PARALLEL, SO THE SLOPE IS THE SAME Im THE CHANGE OF BUNDLE IS DUE ENTIRELY TO THE FALL IN INCOME. A B THIS IS THE INCOME EFFECT max cin. x Cinema

28. INCOME AND SUBSTITUTION EFFECTS The overall effect BY COMBINING THE TWO, ONE GETS THE OVERALL EFFECT Meals max meal x 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 Im A B max cin. x Cinema

29. INCOME AND SUBSTITUTION EFFECTS THIS TYPE OF APPROACH IS FUNDAMENTAL TO MICRO-ECONOMIC ANALYSIS ANY PRICE 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)