Econ 100A Midterm #1 Review Session

1

Hemaxi Desai, Chen Meng, Michael Nguyen-Mason, Amy Qin

Student Learning Center Econ Program● Courses offered: Econ 1, 2, 100A, 100B, 136, 140

● Work closely with professors from each course to tailor materials accordingly

● Weekly Drop-in hours: Mon - Thurs, 10 - 2pm

● Pod Tutoring, Study Groups, and Review Sessions for Exams

○ 100A pod: Friday 3-4 pm | Sign-up link on facebook page and SLC Econ site

● Visit and Like us at our Facebook page: SLC ECON SUPPORT TEAM

2

AgendaMain Topics:

1. Indifference Curve2. Inferior vs. normal, complements vs. substitutes 3. Utility Maximization4. Income and Substitution Effect5. Marshallian and Hicksian Demand6. Elasticity 7. Engel curve

3

T/ F Questions1. Hicksian demand curve is more elastic than Marshallian demand curve when

a good is normal.

4

Effect of Falling Prices on Different Goods ● Normal Good

As your income goes up, you consume more of it. Substitution and Income effect go into the same direction.

● Inferior GoodAs your income goes up, you consume less of it. Substitution and income effect go into opposite direction

● Giffen GoodA special type of inferior goodAs price of a good rises, you consume more of it. Substitution and income effect go into opposite direction and the magnitude of income effect is larger.

5

● Marshallian demand is the normal demand curve that accounts for both substitution and income effect, while Hicksian is just substitution effect.

● For a normal good, substitution and income effect go in the same direction so quantity change for Marshallian demand is larger compared to the Hicksian demand (given a price change).

● Therefore, Marshallian demand curve is flatter.

FALSE!

6

BC0BC1

T/ F Questions2. If pizza and soda are perfect complements, the utility maximization point would be a corner solution.

7

Perfect complements | Perfect Substitutes

● Perfect complements: one’s well-being depends on having both goods in set quantities

● Perfect substitutes: one is indifferent between consuming one good or another (you consume the

cheaper good)

8

Corner vs Interior Solution: Perfect Complements:

★ Utility Maximization is where the budget line is tangent to the highest indifference curve

9

FALSE!

T/ F Questions3. Alice likes sushi (the x-axis good) and the more money she has, the more sushi she will eat. If the price of sushi increases, the Engel curve for sushi shifts to the right.

10

● Engel curves relate the QUANTITY (X) of a good consumed to INCOME (Y) holding price constant.

● NORMAL: the Engel curve is upward sloping

● INFERIOR: the Engel curve is downward sloping

● Higher income, larger quantity -> normal good

● At any given income level, as the price of the good increases, Alice will consume less of it (both income and substitution effect)

● Shift to the left11

FALSE!

T/ F Questions4. Along a single linear demand curve, elasticity is increasing as quantity consumed is increasing.

Price elasticity of Demand (PED) refers to the degree of responsiveness of quantity demanded of a good given a change in the price of the good itself, ceteris paribus.

Elasticity Value

12

13

FALSE!

T/ F Questions5. The optimal bundle obtained by minimizing expenditure is different than the optimal bundle obtained by maximizing utility.

14

FALSE! The bundle for expenditure minimization and profit maximization are the same → the tangent point of the highest indifference curve and given budget constraint. We solve both problems by the Lagrangian method.

For expenditure minimization, utility is held constant as the constraint; for profit maximization, income is held constant.

Profit maximization: L = U(X,Y) + λ(I - Px X - Py Y)

Cost / Expenditure minimization: L = I(X, Y) + λ(U - U(x))

15

T/ F Questions6. If Hicksian demand is downward sloping, then Marshallian demand must be downward sloping as well.

16

Hicksian demand (compensated demand curve): substitution effect

- Utility held constant- Always downward sloping

Marshallian demand: substitution effect + income effect

- Income held constant- Downward sloping for normal good & inferior good- Upward sloping for Giffen good

17

FALSE!

T/ F Questions7. If price elasticity of demand is negative then the good must be normal.

18

FALSE!Elasticity =( Q / P) * P/Q

P, Q > 0

Price elasticity of demand is negative:

Q / P < 0

Price increases → Quantity decreases

=> the good can be either a normal good, or an inferior good (Income up, quantity decreases)

=> However, the good cannot be a Giffen good 19

T/F Questions8. A good cannot be both normal and inferior.

20

False!Backward bending engel curve.

For a certain level of income, Corolla would be a normal good. However, once your income gets high enough, you might want something more fancy and Corolla became inferior.

21

T/F Questions9. An inferior good cannot be represented with a Cobb-Douglas utility function.

22

True!Recall the optimal bundle for Cobb-Douglas:

X* = αI/Px

Y* = (1- α)I/Py

When we take the partial derivative of Qx or Qy with respect to I, we always get a positive number, so they are normal goods.

23

Cobb Douglas Utility Function

24

T/F Questions10. If cereal and milk are perfect complements and the price of milk decreases, the substitution effect is smaller than the income effect.

25

For perfect complements, substitution effect is always 0.

And as we can see on the graph, the

income effect is always positive, which

means perfect complements are always

normal goods.

26

True!

T/F Questions11. An increase in income will shift both the uncompensated and compensated demand curves.

27

True!When income increases, the original budget constraint shifts out and the original bundle contains more of both X and Y. Therefore, if we look at the demand graph, at a certain price of Px, we will buy more X, so it can be considered as an parallel shift to the right of both demand curves.

Easier way to think is to follow the ideas in Econ 1. When a variable that’s not on the axis changes, the curve will shift. Here, since income increases and on the axis, we only have Qx and Px, both of the demand curves shifts upward.

28

Short Answer #1What is the ECONOMIC meaning of the equality MUx/PX = MUy/PY? Explain when it might not be valid.

The marginal utility per dollar spent on good X is equal to the marginal utility per dollar spent on good Y.(The last dollar spent on either good, gives the same level of marginal utility)

This means that the slopes of MRS and MRT are equal --- profit maximization bundle. This is violated whenever we have corner solution. (Ex. Perfect Substitute.)

29

Short Answer #2Trace the demand curve for a Giffen good by using the 2-panel graph. On the top panel, find two optimal bundles for different prices. On the bottom panel, plot the corresponding demand curve. Make sure your axes are labeled.

30

● When the price of X decreases, the budget

constraint rotates to the right, and substitution effect is the horizontal distance between bundle A and B.

● Because the question is asking for a Giffen good, we know the income effect is to the opposite direction and is larger than substitution effect, so we end up with final bundle C to the left of A.

● On the lower graph, we have two bundles A and C for before and after the price change of X. Therefore, we can trace the demand curve by connecting those two bundles.

AB

C

A

C

31

Effect on Giffen Goods

Short Answer #3

32

Solutionα α

α

33

Short Answer #4

34

Short Answer #4 a Solution

35

Pr increases

Short Answer #4

36

Short Answer #4 b solution

37

Income increase

BC0 BC1

A

B

Short Answer #5

38

Short Answer #5 solution

39

Long Answers #1

40

Long Answers #1

41

Long Answers #1

42

Long Answers #1

43

Long Answers #1

→

→

→

44

Long Answers #1

45

Long Answers #1

46

Long Answers #1d. How much more money is needed to maintain the same utility?

47

Long Answers #1In order to find the substitution bundle, we need to find bundle at NEW price, OLD utility

We already calculated the substitution bundle in part c, which is (X, Y) = (4.2, 7.5). Therefore, the total expenditure = (2 x 4.2) + (1 x 7.5) = $15.9

Thus, 15.9 - 11 = 4.9, which is the extra amount that is needed to keep the same utility.

48

Long Answers #1e. How much more money is needed to afford the original bundle?

49

Long Answers #1The original bundle is (6,5) and so the total expenditure after the price change would be 6 x 2 + 5 x 1 = 17

Thus, 17 - 11 = 6, which is the extra amount needed.

50

Long Answers #1f. Set up and solve the expenditure minimization problem.

51

Long Answers #1

52

Plug the relationship in the budget constraint E = Px * X + Py * Y to find the optimal bundle. Y* = (E - Py) / 2Py X* = (Py + E) / 2Px

Plug the optimal bundle into utility function U = X(1+Y) = [(Py + E)/2px] [1 + (E-Py)/2Py]= (Py + E)^2 / 4PxPy

Then solve for E: E = sqrt(4UPxPy)-py

Note: When we take the partial derivative of E with respect to Px and Py, we get the compensated demand function.

Long Answer Question #2Jason is in charge of the government agency that supplies electricity to the city. Electricity is sold in units of kilowatt-hours (kwh). The price per kwh is PE = $1.00. Assume that the average resident of the city has a monthly budget of $200 to spend on either kilowatts of electricity, E, or dollars-worth of all other goods, Y. To make sure that very poor residents get their basic electricity needs met, the city council has recently passed a law whereby each resident can use up to 25 kwh of electricity for free each month. Jason has to decide how to set the exact pricing policy for this law. He has two plans, plan A and plan B.

53

Long Answer Question #2Jason is in charge of the government agency that supplies electricity to the city. Electricity is sold in units of kilowatt-hours (kwh). The price per kwh is PE = $1.00. Assume that the average resident of the city has a monthly budget of $200 to spend on either kilowatts of electricity, E, or dollars-worth of all other goods, Y. To make sure that very poor residents get their basic electricity needs met, the city council has recently passed a law whereby each resident can use up to 25 kwh of electricity for free each month. Jason has to decide how to set the exact pricing policy for this law. He has two plans, plan A and plan B.

So from this question, we can deduce the following:

I = 200, PE = $1.00 , Py = $1.00

54

Long Answer - Part A Plan A) For the first 25kwh each month, electricity is free. For any additional units after 25, the price is $1.00.

i) Compute the monthly budget constraint for the average resident under Plan A.

ii) Graph this budget constraint, with electricity on the horizontal axis.

55

Long Answer - Part A a) For the first twenty-five units of E there is no expenditure on E so the consumer can spend their

entire budget on all other goods. Thus, the budget constraint is simply Y = I/Py = 200/1 = 200. For units of E above twenty-five the budget constraint must take expenditure on E into account, but the first twenty-five units don’t add to expenditure.

Thus, the budget constraint is (E − 25) + Y = 200.

Solving for Y we get Y = 225 − E, so the full budget constraint in terms of Y is:

Y = 200 if E ≤ 25

Y = 225 – E if E > 25

56

Long Answer - Part B Plan B) If a resident uses 25 kwh or less in a given month, it is free. But if a resident uses more than 25 kwh in a given month, they have to pay the regular price, $1.00, for every kwh they use, including the first 25.

i) Compute the monthly budget constraint for the average resident under Plan B.

ii) Graph this budget constraint on a new graph, with electricity on the horizontal axis.

57

Long Answer - Part B

≤

−

58

Long Answer - Part C (1 of 4)Question: Jason wants to minimize the increase in electricity consumption caused by the new law. Without knowing anything about consumer’s preferences, which plan would you advise him to choose? Explain.

Nature of Good: Electricity should be considered a normal good because with an increase in income, people should consume more electricity. Some may argue that electricity is a quasilinear good since an increase in income may not affect the level of consumption, but we will see that this would not change our response significantly.

Nature of Consumers: The different possible consumption bundles are

● Consumers who are currently using less than 25kwh per month● Consumers who are using around 25kwh per month● Consumers who are using above 25kwh per month

Let us now assess what happens for each type of consumers under Plan A and Plan B. After which, we will compare the two outcomes.

59

Long Answer - Part C (2 of 4)Question: Jason wants to minimize the increase in electricity consumption caused by the new law. Without knowing anything about consumer’s preferences, which plan would you advise him to choose? Explain.

PLAN A:

Consumers who are currently using less than 25kwh per month

● Consumption should go up under Plan A because budget constraint has been pushed out. Intuitively, if the first 25kwh is free for me and I only start paying the regular rate after I hit the 25kwh benchmark, I would most certainly increase my electricity consumption (or at the least not change the level of electricity consumption).

● Using this same intuition, we realize consumers who are using around 25kwh per month or above 25kwh per month would behave similarly since their budget constraint has been pushed out.

60

Long Answer - Part C (3 of 4)Question: Jason wants to minimize the increase in electricity consumption caused by the new law. Without knowing anything about consumer’s preferences, which plan would you advise him to choose? Explain.

PLAN B:

Consumers who are currently using less than 25kwh per month & using around 25kwh per month

● May not change or increase until at most 25kwh per month, if not they have to start paying. In fact, those using slightly more than 25kwh per month may choose to reduce their consumption to 25kwh so that they don’t pay anything (possibly gain a higher overall utility).

Consumers who are currently using more than 25kwh per month:

● No change to their original budget constraint since they are paying for every unit of electricity as before.

61

Long Answer - Part C (4 of 4)Summary Table of Economic Outcomes for Plan A & Plan B

62

Consumers Usage /Electricity Plans

< 25kwh ~ 25kwh > 25kwh Overall Effect

Plan A No change or increase

consumption

No change or increase

consumption

No change or increase consumption

At best no change in electricity

consumption but likely to increase

overall

Plan B No change or increase

consumption but limited to 25kwh

Those slightly above 25kwh likely to

reduce consumption

No change More likely to reduce electricity

consumption overall

Long Answers #3

63

Long Answers #3

64

1.

65

Long Answers #3

2. Let I = 1000, k = 100, a = 0.5 and Py = 2

a.

b.

C.

66

Long Answers #3

3. Now let I = 100 and the rest of the parameters are the same

a. I = 100 < Py * k = 200 so in this situation, this is a corner solution. b.

c.

67

Long Answers #3

Long Answers #4

68

Long Answers #4⅔

⅓

69

Long Answers #4

70

Long Answers #4

71

Long Answers #4

72

Long Answers #4

73

For Marshallian demand: e = Elasticity = ( Q / P) * P/Q = (-200/2)*(2/400) = -0.5 For Hicksian demand: e = Elasticity =( Q / P) * P/Q = (-100/2)*(2/400) = -0.25 The absolute value of the Marshallian price elasticity of demand is bigger, which means it is more elastic.

Long Answers #4

74

Long Answers #4

75

Any Questions?

76

Student Learning Center Econ Program● Courses offered: Econ 1, 2, 100A, 100B, 136, 140

● Work closely with Professors from each course to tailor materials accordingly

● Weekly Drop-in hours: Mon - Thurs, 10am-2pm

● Pod Tutoring and Review Sessions for Midterms and Finals

● Visit and Like us at our Facebook page: https://www.facebook.com/econatslc/?fref=ts

77

THANK YOU