Consumer’s Optimal Choice

Question 1

Consumer rational choice concept, and how this is graphically shown

Answer 1

Consumer chooses an optimal bundle given their budget constraint.

Shown by the indifference curve tangent to budget line

Question 2

When is tangency condition untrue (4)

Pg 23&24, learn diagrams

Answer 2

Kinky tastes (linear preferences IC’s have no tangency)
Multiple tangencies (one tangental point may not be optimal)
Boundary solution (optimal consumption may be consuming 0 units of one good so not tangental)
Concave preferences (pg29)

Question 3

So tangency condition (optimal bundle is where IC and BC are tangental) is a sufficient condition ONLY for interior solutions:

What does interior mean??

Answer 3

Positive amounts of both goods! (Unlike boundary solution)

Question 4

So the optimal bundle is the demanded bundle.

Express demand functions for bundle x and y.

Answer 4

X (Px,Py,m) and Y(Px,Py,M)

(I.e each bundle X and Y are functions of price and income)

Question 5

Perfect substitutes graph pg 27.

What good should we consume?
What would demand functions be if prices are equal, p₁>p₂ or p₁<p₂?

Answer 5

We only consume the cheaper good. (Red pencils)

If equal prices, demand function x = any number between 0 and M/P₁ (maximum quantity of X upon the budget line) can be the optimal choice.

If p₂>p₁ , we consume good 1, so demand function is
x= m/p₁

If p₂<p₁ demand function is x=0

Question 6

What would be the demand function/optimal choice for bad good Y?

Answer 6

All income used for the “good” good:

Demand function is x=m/px

Question 7

Optimal choice for neutral good Y

Answer 7

All income used for the “good” good:

x=m/px

Question 8

Demand function/ Optimal choice when there is concave preferences.

(Pg29)

Answer 8

Optimal choice is the boundary point

When X=0 or Y=0
(On the axis)

Question 9

How to find optimal choice for discrete goods

Answer 9

Draw budget constraint and indifference curve to identify it visually. (highest intersection of BC and IC)

Question 10

2 maths ways

Answer 10

Lagrangian
Tangency condition

Question 11

Tangency condition equation and steps

Answer 11

Slope of budget line = slope of indifference curve

-Px/Py = MRS = -MUx/MUy

1.Find MUx and MUy by differentiating.
2.Then sub back into Px/Py = MUx/MUy
3. Find x and y in terms of Px,Py and M by rearranging step 2 using the budget constraint expression (shown pg39)

Question 12

Interpretation if BC slope and IC slope do not equal. (I.e not at the optimal consumption level)

If Px/Py > MRSyx:

If Px/Py < MRSyx:

Answer 12

If Px/Py > MRSyx the consumer increases utility by consuming more Y

If Px/Py < MRSyx the consumer increase utility by consuming more X

Question 13

Optimal choice examples (in textbook)

Go back and cover these examples (relearn Lagrange method) also recognise economic theory is needed for 1st class

Question 14

Now we want to see the impact of an income tax vs quantity tax on a consumer (for the same total tax collected)

Quantity tax into an optimisation equation (let good X be the one taxed)

Answer 14

Step 1: Put into budget constraint
(Px+t) + PyY = M

(Px+t) is the price of X + tax added on

Question 15

We need to add government revenue in this equation

Answer 15

Revenue (R) = tx

I.e tax per unit x quantity of the taxed good x.

Question 16

Express Income tax into an optimisation equation

Answer 16

As income tax is deducted from consumer’s income (M)

Use the budget constraint:
PxX + PyY = m-R*

And remember R* = tx* so it becomes

PxX + PyY = m - tx*

Question 17

Learn taxes added optimisation graph (for income and quantity tax) pg 46

Answer 17

Income tax - influences m so slope unchanged, intercept falls.

Quantity tax - slope changes as price of X increases so steepens as we can now afford less of good X.

We can see that income tax is better for the consumer since it can achieve a higher I.C than the quantity tax.

Question 18

If both income and quantity tax provide the same revenue for the government, what is best for the consumer in this case?

And what assumptions have been made for this consumer? (3)

Answer 18

Income tax is better for the consumer (able to gain higher utility with a higher indifference curve)

We have assumed
Uniform preferences
Constant income
No supply side response to the tax