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Microeconomics Pre-sessional September 2015

Microeconomics Pre-sessional September 2015. Sotiris Georganas Economics Department City University London. Organisation of the Microeconomics Pre-sessional . Introduction 10:00-10:30 Demand and Supply 10:30-11:10 Break Consumer Theory 11:25-13:00 Lunch Break

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Microeconomics Pre-sessional September 2015

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  1. Microeconomics Pre-sessionalSeptember 2015 Sotiris Georganas Economics Department City University London

  2. Organisation of theMicroeconomics Pre-sessional • Introduction10:00-10:30 • Demand and Supply 10:30-11:10 Break • Consumer Theory11:25-13:00 Lunch Break • Problems – Refreshing by Doing 14:00-14:30 • Theory of the Firm14:30 -15:30 Break • Problems – Refreshing by Doing 15:45 -16:30

  3. Consumer Theory • Description of Consumer Preferences • Utility Function • Indifference Curves • Marginal Rate of Substitution • Consumer Maximisation Problem • Individual and Aggregate Demand Curves

  4. Description ofConsumer Preferences Consumer Preferences tell us how the consumer would rank (that is, compare the desirability of) any two combinations or allotments of goods, assuming these allotments were available to the consumer at no cost These allotments of goods are referred to as baskets or bundles. These baskets are assumed to be available for consumption at a particular time, place and under particular physical circumstances.

  5. Basket of Food and Clothing Units of Clothes A  (1,5 ) C  (4,5 ) • • B  (8,1 ) • Units of Food

  6. Properties ofConsumer Preferences Completeness Preferences are complete if the consumer can rank any two baskets of goods (A preferred to B; B preferred to A; or indifferent between A and B) Transitivity Preferences are transitive if a consumer who prefers basket A to basket B, and basket B to basket C also prefers basket A to basket C Monotonicity Preferences are monotonic if a basket with more of at least one good and no less of any good is preferred to the original basket (more is better?)

  7. The Utility Function The utility functionassigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets Utility is an ordinal concept: the precise magnitude of the number that the function assigns has no significance

  8. ExampleBasket of One Good

  9. Marginal Utility Marginal utility of a good x is the additional utility that the consumer gets from consuming a little more of x when consumption of all the other goods in the consumer’s basket remains constant U/x (y held constant) = MUx U/y (x held constant) = MUy Marginal utility is measured by the slope of the utility function The principle of diminishing marginal utilitystates that marginal utility falls as the consumer gets more of a good

  10. ExampleBasket of One Good The more, the better?

  11. ExampleBasket of One Good The more, the better?

  12. ExampleBasket of One Good Diminishing marginal utility?

  13. Indifference Curves An Indifference Curve (or Indifference Set) is the set of all baskets for which the consumer is indifferent An Indifference Mapillustrates a set of indifference curves for a given consumer

  14. ExampleSingle Indifference Curve

  15. 3D Graph of a Utility Function

  16. Properties ofIndifference Maps Completeness Each basket lies on one indifference curve

  17. Properties ofIndifference Maps Completeness Each basket lies on one indifference curve Transitivity Indifference curves do not cross

  18. Properties ofIndifference Maps

  19. Properties ofIndifference Maps Completeness Each basket lies on one indifference curve Transitivity Indifference curves do not cross Monotonicity Indifference curves have negative slope and are not “thick”

  20. Properties ofIndifference Maps Completeness Each basket lies on one indifference curve Transitivity Indifference curves do not cross Monotonicity Indifference curves have negative slope and are not “thick”

  21. Properties ofIndifference Maps Completeness Each basket lies on one indifference curve Transitivity Indifference curves do not cross Monotonicity Indifference curves have negative slope and are not “thick”

  22. AssumptionAverage Preferred to Extremes y indifference curves are bowed toward the origin (convex to the origin) A • (.5A, .5B) • IC2 • IC1 B x

  23. What does the slope mean? y A • • IC1 B x

  24. Marginal Rate of Substitution The marginal rate of substitution is the decrease in good y that the consumer is willing to accept in exchange for a small increase in good x (so that the consumer is just indifferent between consuming the old basket or the new basket) The marginal rate of substitution is the rate of exchange between goods x and y that does not affect the consumer’s welfare MRSx,y = -y/x (for a constant level of utility)

  25. ExampleMarginal Rate of Substitution y A  B A B 1 1/2 U=1 0 x 1 2

  26. y 1 0 x ExampleMarginal Rate of Substitution 1

  27. Indifference curves (usually) exhibit diminishing rate of substitution The more of good x you have, the less of good y you are willing to give up to get a little more of good x The indifference curves get flatter as we move out along the horizontal axis and steeper as we move up along the vertical axis

  28. Special Functional Forms 1. Cobb-Douglas: U(x,y) = Axy where:  +  = 1; A, , positive constants 2. Perfect substitutes U(x,y) = ax + by 3. Perfect complements U(x,y) = min {ax, by} 4. Quasi-linear: U(x,y) = v(x) + by

  29. y Preference direction IC2 IC1 x 1. Cobb-Douglas: U = Axy where:  +  = 1; A, , positive constants MRS = "

  30. 2. Perfect substitutes U(x,y) = ax + by 3 Pepsi MRS = 2 Example: U=x+y 1 0 COKE 1 1 2 3

  31. 3. Perfect complements U(x,y) = min {ax, by} MRS = Example: U=10min{x,y} U=10 1 0 x 1 2

  32. 4. Quasi-linear: U(x,y) = v(x) + by Where: b is a positive constant. MUx = v’(x) , MUy = b, MRSx.y = v’(x)/ b

  33. The Budget Constraint Assume only two goods available (x and y) Px Price of x Py Price of y I Income Total expenditure on basket (X,Y): PxX + PyY The basket is affordable if total expenditure does not exceed total income: PxX + PyY ≤ I

  34. ExampleA Budget Constraint Y, Clothes • Two goods available: X and Y • I = $10, Px = $1,Py = $2 • 1X+2Y=10 Or Y=5-1/2X A • I/PY= 5 • D Slope -PX/PY = -1/2 • C B • X, Food I/PX = 10

  35. Definitions The set of baskets that are affordable is the consumer’s budget set: PxX + PyY = I The budget constraint defines the set of baskets that the consumer may purchase given the income available: PxX + PyY  I The budget line is the set of baskets that are just affordable: Y = I/Py – (Px/Py)X

  36. ExampleA Change in Income Y I1 = $10, I2 = $12 PX = $1 PY = $2 Y = 5 - X/2 BL1 Y = 6 - X/2 BL2 6 5 BL2 BL1 10 12 X

  37. ExampleA Change in Price (good Y) If the price of Y rises, the budget line gets flatter and the vertical intercept shifts down If the price of Y falls, the budget line gets steeper and the vertical intercept shifts up Y BL1 5 I = $10 PX = $1 PY1 = $2 , PY2 = $3 Y = 5-X/2…BL1 Y = 3.33 - X/3 …. BL2 3.33 BL2 X 10

  38. Consumer Choice • Assume: • Only non-negative quantities • "Rational” choice: The consumer chooses the basket that maximizes his satisfaction given the constraint that his budget imposes • Consumer’s Problem: • Max U(X,Y) • subject to: PxX + PyY  I

  39. Solving the Consumer Choice • Consumer’s Problem: • Max U(X,Y) • subject to: PxX + PyY  I • The solution could be: • Interior solution (graphically and/or algebraically) • Corner solution (graphically)

  40. Corner Consumer Optimum • A corner solution occurs when the optimal bundle contains none of one of the goods • The tangency condition may not hold at a corner solution • How do you know whether the optimal bundle is interior or at a corner? • Graph the indifference curves • Check to see whether tangency condition ever holds at positive quantities of X and Y

  41. Interior Consumer Optimum Y • B • D • F BL 0 X

  42. Interior Consumer Optimum Y Preference direction • B • D • F U=30 U=10 U=5 BL 0 X

  43. ExampleInterior Consumer Optimum Y 20X + 40Y = 800 800= 20X+40Y (constraint) Py/Px = 1/2 (tangency condition) • Tangency condition: • MRS = - MUx/MUy = -Px/Py • 10 U = 200 0 20 X

  44. ExampleInterior Consumer Optimum • U(X,Y) = min(X,Y) • I = $1000 • Px = $50 • PY = $200 • Budget line • Y = $5 - X/4

  45. ExampleCorner Consumer Optimum Y X + 2Y = 10 0 X

  46. Individual Demand Curves The price consumption curveof good x is the set of optimal baskets for every possible price of good x, holding all other prices and income constant

  47. ExampleA Price Consumption Curve Y (units) 10 PY = $4 I = $40 • PX = 4 X (units) 0 XA=2 20

  48. ExampleA Price Consumption Curve Y (units) 10 PY = $4 I = $40 • • PX = 2 PX = 4 X (units) 0 XA=2 XB=10 20

  49. ExampleA Price Consumption Curve Y (units) 10 PY = $4 I = $40 • • • PX = 1 PX = 2 PX = 4 X (units) 0 XA=2 XB=10 XC=16 20

  50. ExampleA Price Consumption Curve Y (units) The price consumption curve for good xcan be written as the quantity consumed of good x for any price of x. This is the individual’s demand curve for good x 10 PY = $4 I = $40 Price consumption curve • • • PX = 1 PX = 2 PX = 4 X (units) 0 XA=2 XB=10 XC=16 20

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