[PPT] - GPP 501 Microeconomic Analysis for Public Policy Fall 2017 Given PowerPoint Presentation

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GPP501: Lecture Sept 12 1 of 24

GPP 501 Microeconomic Analysis for Public Policy Fall 2017

Given by Kevin Milligan Vancouver School of Economics University of British Columbia Lecture Sept 12th: Demand

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GPP501: Lecture Sept 12 2 of 24

Agenda for today:

1. Go from choice to preference maps.
2. Budget sets.
3. Demand Curves.

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GPP501: Lecture Sept 12 3 of 24

Axioms of choice:

Reminder: why are we going through this?

We want to build up to demand curves and supply curves.
Once we understand demand and supply curves, we can start doing some economic

analysis of policy issues. Q: do you remember the three from last lecture? Q: what did we say about choices that satisfied the three axioms?

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GPP501: Lecture Sept 12 4 of 24

Axioms of choice:

From last time:

1. Completeness
2. Transitivity
3. Reflexivity

Where do we want to go? We want to build a structure for preferences that we can represent in diagrams and in math. To do so, we will need to add more assumptions….

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GPP501: Lecture Sept 12 5 of 24

Axioms of choice:

4. Continuity: assumes that rankings are “smooth”
A technical assumption that assures that preference rankings don’t ‘jump’ around

the edges.

This is necessary in order to write down preference curves.
5. Strong monotonicity: more is preferred to less.
For any comparison, we assume that more is preferred to less.
This can be weakened to “local non-satiation.”
Necessary so that we don’t have ‘fuzzy’ or ‘thick’ comparisons.
6. Convexity: assures ‘well-behaved’ preference curves.
Interior points on a line between two bundles are at least as good as boundary points.
This one is much easier to see in a diagram…..

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GPP501: Lecture Sept 12 6 of 24

Indifference curves:

Each indifference curve shows a

constant level of enjoyment from bundles of x1 and x2.

What does non-monotonicity do?
What does convexity do?
Can indifference curves cross?
Which direction makes us best off?
Is this true even for small jumps?

x1 x2

U1 U0 U2

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GPP501: Lecture Sept 12 7 of 24

Exploring indifference curves:

Does this violate any of the

assumptions?

How would you describe the way

people like to consume x1 and x2?

Any examples come to mind?

x1 x2

U1 U0 U2

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GPP501: Lecture Sept 12 8 of 24

Exploring indifference curves:

Does this violate any of the

assumptions?

How would you describe the way

people like to consume x1 and x2?

Any examples come to mind?

x1 x2

U1 U0 U2

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GPP501: Lecture Sept 12 9 of 24

Agenda for today:

1. Go from choice to preference maps.
2. Budget sets.
3. Demand Curves.

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GPP501: Lecture Sept 12 10 of 24

Budget sets:

We now know how to talk about choices over bundles of goods.

Indifference, utility, preferences.

But which bundle should we choose?

What is our ultimate favourite bundle going to look like under strong monotonicity?
What stops us from getting to that favourite bundle?

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GPP501: Lecture Sept 12 11 of 24

Budget sets:

Our model of choice is much more useful if we put a constraint on resources.

Income
Wealth
Time

We know time is a hard constraint; can’t budge it. But income and wealth—where do they come from?

Complex choices about work, consumption, savings, human capital, and time.
We’ll just work with an endowment economy for now. “Helicopter” money.

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GPP501: Lecture Sept 12 12 of 24

Budget sets:

Imagine we have:

Income set at fixed y.
Goods x1 and x2.
Prices for goods fixed at p1 and p2.

Let’s express this as a budget. 𝑧 ≥ 𝑞1𝑦1 + 𝑞2𝑦2 All choices of bundles of x1 and x2 that satisfy the budget constraint are feasible choices. Q: Why did I use a “≥” sign? Q: Under what assumption would this hold strictly at “=”?

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GPP501: Lecture Sept 12 13 of 24

Budget sets:

What points can we afford?
What points can we not afford?

x1 x2

𝑧 = 𝑞1𝑦1 + 𝑞2𝑦2

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GPP501: Lecture Sept 12 14 of 24

Budget sets:

What happens if I get more y?
Parallel shifts outward of budget line.

x1 x2

𝑧0 < 𝑧1 < 𝑧2 𝑧0 𝑧1 𝑧2

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GPP501: Lecture Sept 12 15 of 24

Budget sets:

If you give up one unit of 𝑦1 you are +

𝑞1 dollars.

This means you can afford

𝑞1 𝑞2 more

units of 𝑦2.

So, the slope of the budget line is:
∆𝑦2

∆𝑦1 =

𝑞1 𝑞2

−1 = −𝑞1 𝑞2

x1 x2

𝑧 = 𝑞1𝑦1 + 𝑞2𝑦2 Slope is

−𝑞1 𝑞2 .

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GPP501: Lecture Sept 12 16 of 24

Agenda for today:

1. Go from choice to preference maps.
2. Budget sets.
3. Demand Curves.

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GPP501: Lecture Sept 12 17 of 24

Putting preferences and budget constraints together

What happens when we combine our diagrams?

Put down a given budget constraint.
What is the best bundle we can afford?
If we do this and then repeat the exercise for different prices of good 𝑦1, we will

trace out a demand curve for 𝑦1.

Let’s give this a shot!

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GPP501: Lecture Sept 12 18 of 24

Putting preferences and budget constraints together

Start with our normal budget constraint.
Which points are feasible for us to

pick?

What points are not feasible?
How should we choose among feasible

points?

x1 x2

𝑧 = 𝑞1𝑦1 + 𝑞2𝑦2

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GPP501: Lecture Sept 12 19 of 24

Putting preferences and budget constraints together

Consider A, B, C, D.
Which is the point we like best if we

could afford any of them?

Considering our budget constraint,

which should we choose?

What is true of the slope of the budget

line and the slope of the indifference curve at the best point?

x1 x2

D C B A

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GPP501: Lecture Sept 12 20 of 24

Let’s redo it for different prices for 𝒚𝟐:

Start off at our initial price for 𝑦1, price

is 𝑞1

0. We choose point 𝐷0 .
Now increase the price to 𝑞1

1>𝑞1 0.

We can afford less now, so budget

constraint swings inward. We can only afford point 𝐷1 now. That has less good 𝑦1.

Note that we can’t necessarily say

whether we consume more/less good 𝑦2.

Finally, tighten prices even more:

𝑞1

2>𝑞1

1. We now choose point 𝐷2.

x1 x2

C0 C1 C2 Slope is

−𝑞1 𝑞2 .

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GPP501: Lecture Sept 12 21 of 24

Demand Curve for 𝒚𝟐:

Note that this is a different graph from

the previous one.

Previous one showed good 𝑦1 and good

𝑦2.

This is just good 𝑦1.

x1 p1

C0 C1 C2

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GPP501: Lecture Sept 12 22 of 24

Demand Curve for 𝒚𝟐:

What happens to demand curve if

incomes go up?

What happens to demand curve if price
f other good goes up?
Does answer change for

substitutes and complements?

What happens to demand curve if price
f good 𝑦1 goes up?

x1 p1

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GPP501: Lecture Sept 12 23 of 24

Concept: Elasticity of demand

How can we characterize whether the change in demand when price changes is big or small?

We use the concept of “elasticity”. We define it this way:

Price elasticity of demand %∆𝑌1 %∆𝑞1 ⁄ .

What is the percentage change in the quantity compared to the percentage change in

price?

We generally use 1.0 as the cutoff between “elastic” and “inelastic”
If greater than 1.0, we call it elastic.
If less than 1, we call it inelastic.

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