1.4 T1

Question 1

When can’t you use tangency condition to maximise (x,y) wrt px, py and m? (Explain 3)

Answer 1

1) Kinky tastes tf optimum consumption bundle has no tangent
2) boundary optimal - the IC becomes tangent to the budget constraint at negative values of one of the goods, but this isn’t possible tf solution is on the x/y axis
3) multiple tangencies - when there are more than one tangency (ie. 3), the tangency condition can be necessary but NOT sufficient

Question 2

Draw diagrams for 3 exceptions to tangency condition

Answer 2

Now

Question 3

When is tangency a sufficient condition for optimum consumption bundle?

Answer 3

When preferences are convex, and X* and Y* are >=0 at OCP

Question 4

What does the demand function do?

Answer 4

Explains the relationship between different demanded consumption bundles and different prices and incomes

Question 5

How is the demand function denoted?

Answer 5

x(px,py,m) and y””

Question 6

What happens to OCP if two goods are perfect subs?

Answer 6

Only the cheaper good will be consumed tf boundary solution (slope IC=-1) (draw diagram!)

Question 7

What do concave preferences imply? Where does this mean the optimum is? (Draw diagram)

Answer 7

That the consumer prefers to consume one good or the other

Optimum at boundary point

Question 8

If good y is a ‘bad good’, what will this mean? And if y is a neutral good?

Answer 8

All income spent in ‘good’ good x:

x=m/px BOTH CASES

Question 9

Why aren’t perfect complements solved by tangency?

Answer 9

There is no tangent tf at point where budget touches corner of IC

Question 10

How do you solve discreet good OCP?

Answer 10

No tangency tf have to compare utility of different consumption bundles (see diagram)

Question 11

2 types of mathematical solutions to well behaved preferences (interior solutions only!)?

Answer 11

Mathematical tangency condition (slope of BL = slope of IC)

Lagrangian solution (learn/see notes)

Question 12

How does the ratio of prices to MRS affect the consumers actions?

Answer 12

If p(x)/p(y) < MRS then consumer will increase utility by consuming more of y & vice versa

Question 13

What are homothetic preferences?

Answer 13

When a consumer will spend equal amounts on good x and good y irrespective of prices of income (see examples in slides)

Question 14

How does the budget constraint change for:

a) including a quantity tax
b) including an income tax?

Answer 14

a) eg. p(x) becomes p(x+t)

b) R is deducted from consumer income tf m-R=“”

Question 15

Why do consumers prefer income tax to quantity tax?

Answer 15

Because the quantity tax affects their choices - they like freedom of choice (see slides)

Question 16

Limitations of analysis regarding the type of tax the consumer would prefer? (5)

Answer 16

Only considered 1 consumer
Assumed uniform preferences
Simplified taxes
Assumed income constant
Not studied supply side response to tax

Question 17

How to solve for OCP when utility is linear?

Answer 17

Draw initially to visualise the solution
Then compare the absolute value of the MRS with p(x)/p(y)

If MRS is larger than ratio of prices only consume good x

If MRS is smaller than the ratio of prices only consume good y