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Budget constrain
- 1. The budget constraintand 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: • If we only look at 2 goods (Same simplification as last week), it can be expressed as: n i i i 1 I p x 1 1 2 2I p x p x
- 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: 50 5 tickets 10 meals 1 1 2 2I p x p x
- 5. The budget constraint Meals Cinema max mealx max meal meal I x p Maximum amount of meals you can buy Diagram in “consumption space”
- 6. The budget constraint max cin. cin. I x p Maximumamount of cinema tickets you can buy max cin.x Cinema Meals max mealx
- 7. The budget constraint max cin.xCinema Meals max mealx Budget constraint
- 8. The budget constraint max cin.xCinema Meals max mealx 1 1 2 2I p x p x 2 1 2 1 1 pI x x p p The budget constraint is Dividing by p1 and rearranging: cin. meal cin. meal meal pI x x p p slope intercept
- 9. The budget constraint Anybundle within the budget constraint is affordable , but not all the budget is spent (C,D). Any bundle beyond the budget constraint cannot be afforded (H,G). C H D G Any bundle on the budget constraint is affordable and ensures all the budget is spent (E,F). max cin.x Cinema Meals max mealx F E
- 10. The budget constraint max cin.xCinema Meals max mealx Budget constraint Budget set
- 11. 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) 2 1 2 1 1 pI x x p p
- 12. The budget constraint max cin.xCinema Meals max mealx Effect of a fall in income (I)
- 13. The budget constraint max cin.xCinema Meals max mealx Effect of a rise in income (I)
- 14. The budget constraint max cin.xCinema Meals max mealx Increase in the price of cinema tickets
- 15. The budget constraint max cin.xCinema Meals max mealx Decrease in the price of cinema tickets
- 16. Lets think aboutthese things • Budget constraint equation • Slope of budget line – Px / Py • budget line is of 45 ° if??? • Shifts in line can be caused by??? • Shows purchasing power of indivisuals • Budget line and what it represents
- 17. Questions A budget constraint a.showsthe prices that a consumer chooses to pay for products he consumes. b.shows the purchases made by consumers. c.shows the consumption bundles that a consumer can afford. d.represents the consumption bundles that give a consumer equal satisfaction.
- 18. A consumer thatdoesn't spend all of her income a.would be at a point outside of her budget constraint. b.would be at a point inside her budget constraint. c.must not be consuming positive quantities of all goods. d.must be consuming at a point where her budget constraint touches one of the axes.
- 19. The following diagramshows a budget constraint for a particular consumer. If the price of x is $10, what is the price of y? a.$15 b.$25 c.$35 d.$70
- 20. Which of the graphsin the figure reflects a decrease in the price of good X only? a.graph (a) b.graph (b) c. graph (c) d.graph (d)
- 21. Which of the graphsin the figure reflects an increase in the price of good Y only? a. graph (a) b.graph (b) c. graph (c) d.graph (d)
- 22. Which of the graphsin the figure could reflect a decrease in the prices of both goods? a. graph (a) b.graph (b) c. graph (c) d.graph (d)
- 23. • A halvingof the prices good A and good B has the same effect on the budget line as doubling the income. Is this sentence true or false? Show it by using the equation of the budget line. • What about the opposite? Doubling the prices good A and good B has the same effect on the budget line as halving of the income.
- 24. Suppose the priceof pizza is $10, the price of cola is $1, and the consumer’s income is $50. In addition, suppose the consumer’s budget constraint measures pizza on the horizontal axis and cola on the vertical axis. 1) If the price of cola doubles to $2, then the a. budget constraint intersects the vertical axis at 25 colas. b. slope of the budget constraint rises to -2. c. budget constraint intersects the vertical axis at 100 colas. d. budget constraint shifts inward in a parallel fashion. 2) If the consumer's income rises to $60, then the budget line for pizza and cola would a. now intersect the horizontal axis at 6 pizzas and the vertical axis at 60 colas. b. not change. c. now intersect the horizontal axis at 4 pizzas and the vertical axis at 16 colas. d. rotate outward along the cola axis.
- 25. Answer the followingquestions based on the table. A consumer is able to consume the following bundles of rice and beans when the price of rice is $2 and the price of beans is $3. RICE BEANS 12 0 6 4 0 8 a. How much is this consumer's income? b. Draw a budget constraint given this information. Label it B. c. Construct a new budget constraint showing the change if the price of rice falls $1. Label this C. d. Given the original prices for rice ($2) and beans ($3), construct a new budget constraint if this consumer's income increased to $48. Label this D.
- 26. Draw a budgetconstraint that is consistent with the following prices and income. Income = 200 PY = 50 PX = 25 a. Demonstrate how your original budget constraint would change if income increases to 500. b. Demonstrate how your original budget constraint would change if PY decreases to 20. c. Demonstrate how your original budget constraint would change if PX increases to 40.
- 27. Evaluate the followingstatement, "Warren Buffet is the second richest person in the world. He doesn't face any constraint on his ability to purchase commodities he wants."
- 28. The budget constraintand choice The budget constraint The optimal consumer choice Income and substitution effects
- 29. The optimal consumerchoice • 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
- 30. The optimal consumerchoice max cin.x Cinema Meals max mealx Which is the best bundle ? F Optimal bundle C D E B A
- 31. The optimal consumerchoice max cin.x Cinema Meals max mealx The budget constraint is tangent to the indifference curve at F F Definition of the MRS at F !!!
- 32. The optimal consumerchoice • 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
- 33. The optimal consumerchoice • 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 2 2 1 2 1 21 1mU p MRS mU p mU mU p p
- 34. The optimal consumerchoice max cin.x Cinema Meals max mealx Example of optimal choice with concave preferences F G The optimal solution is a “corner solution”
- 35. The budget constraintand choice The budget constraint The optimal consumer choice Income and substitution effects
- 36. Income and substitutioneffects • 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
- 37. Income and substitutioneffects • 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 relatively cheaper max cin.x Cinema Meals max mealx An increase in the price of cinema tickets has 2 effects : A
- 38. Income and substitutioneffects • 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 ? max cin.x Cinema Meals max mealx A B Effect of an increase in the price of cinema tickets on consumer choice
- 39. Income and substitutioneffects • 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) max cin.x Cinema Meals max mealx A B In order to separate the 2 effects, we add an imaginary budget constraint Im
- 40. Income and substitutioneffects • 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 max cin.x Cinema Meals max mealx A B The substitution effect Im
- 41. Income and substitutioneffects • 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 max cin.x Cinema Meals max mealx A B The income effect Im
- 42. Income and substitutioneffects • 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 max cin.x Cinema Meals max mealx A B The overall effect Im
- 43. Income and substitutioneffects • 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)
Editor's Notes
- #18 C
- #19 B
- #24 Initial budget line: M = PxX + PyY New budget line: · Halving of the prices: M = PxX + PyY 2 (Multiplying by 2) 2M = PxX + PyY · Doubling the income: 2M = PxX + PyY Result: Halving of the prices and doubling the income result in the same budget line. Sentence is true. Initial budget line: M = PxX + PyY New budget line: · Doubling the prices: M = 2(PxX + PyY) (Dividing by 2) M 2 = PxX + PyY · Halving of the income: M 2 = PxX + PyY Result: Doubling the prices and halving of the income result in the same budget line. Sentence is true, too.