Consumer Theory- Optimal Choice

Question 1

With well behaved goods hat which point on a graph signifies the consumer’s best bundle?

Answer 1

The point at which the budget curve is tangent to the higher indifference curve.

Question 2

Is tangency necessary for optimal choice ?

Answer 2

No, it is not sufficient for kinky tastes, multiple tangicies and boundary soloutions. Kinky tastes such as perfect compliments do not have a tangent so it is insufficient. If there are multiple tangicies then the highest tangency is the optimal choice, therefore tangency alone is inefficient. A boundary solution means the optimal solution has 0 units of one good therefore the budget line is not tangent to the indifference curve.

Question 3

When is tangency sufficient ?

Answer 3

When the indifference curve is convex.

Question 4

What solution does perfect substitutes have ?

Answer 4

If PY>PX then the boundary solution is on the X axis. If PY

Question 5

What is the boundary solution for a bad good?

Answer 5

It is a boundary solution as all income will be spent in the good good.

Question 6

What is the optimal solution for a bundle with a neutral good ?

Answer 6

All the money is spent on the good good so it’s a boundary solution.

Question 7

What is the optimal choice for concave preferences?

Answer 7

The optimal choice is a boundary solution.

Question 8

How can we find the optimum choice of consumption ?

Answer 8

• Graphically
• Tangency method
• lagrangian method

Question 9

Describe the tangency method to find the optimum bundle where utility is maximised at Max U= 2xy
Subject to the constraint XPx +YPy=M and x and y must be bigger than 0.

Answer 9

The slope of the budget line= the slope of the indifference curve. 
-Px/Py= -MUx/MUy
Px/Py= 2y/2x
Px/Py= Y/X
XPx=YPy 
Sub in XPx+YPy=m
XPx + XPx=m
2XPx=m
X=m/2Px

Question 10

What is the optimisation problem ?

Answer 10

The consumer wishes to maximise their utility subject to their budget constraint.
MaxU(x,y)
YPy+XPx=m

Question 11

What is the optimal choice of good y and x when maximising utility = 2xy under the constraint XPx+YPy = m.

Answer 11

Lagrangian method dictates=
L= MaxU(x,y) -^(budget constraint )
Where ^ is the Lagrangian multiplier. 
So
L=Max(2xy) -^(XPx+XPy-m) 
We then take partial derivatives of L with respect to x, y and the lagrangian multiplier,^. 
dL/dX=2y-^Px.   dL/dY= 2x-^Py.  dL/d^= XPx+YPy-m. All these are set to equal 0. 
So
2y=^Px 2x=^Py
(2y=^px)/(2x=^Py)
y/x=Px/Py
YPy=XPx
Sub this in m=XPx+YPy