ECON XXXXXXXXXXClass Problems Block 3. Topics covered: Consumer theory. NB: Where the question is multiple choice you still need (for the purposes of these 1001 classes, but not in the end of term...

Class problem block 3, Q3
Class problem block 3, Q3
3. In the field of financial management it has been observed that there is a trade-off between the rate of
eturn that one earns on investments and the amount of risk that one must bear to earn that return. Putting
isk on the horizontal axis and the rate of return on the vertical:
a. draw a set of indifference curves between risk and return for a person that is risk averse (a person that
does not like risk).
Here, utility is a function of return (m) and risk (s). As the individual loves return, the marginal utility of return (Mum)>0 .
A risk averse person doesn’t like risk, i.e, its undesirable for him. So, marginal utility of risk (MUs)<0.
Along an IC, we must have,
U^=U(r,s)
Totally differentiating both sides, we have,
0=MUmdm+MUsds
Or, dm/ds=-MUs/Mum>0
So, the indifference curve will be upward rising.
Since return is desirable for him, the individual will accept a unit of risk if more than a unit of return is given to him. So, the IC will be convex to return axis. The IC will also have a positive intercept on return axis as the bundles with positive return and 0 risk is always desirable to him.
Since at least on commodity is desirable, IC closer to return axis gives higher level of satisfaction.
. draw a set of indifference curves for a person that is risk neutral (a person that does not care about
isk one way or the other).
U^=U(r,s)
Totally differentiating both sides, we have,
0=MUmdm+MUsds
Or, dm/ds=-MUs/Mum>0
So, IC will be upward rising.
In this case, risk is still undesirable for the individual, but as he is risk neutral, marginal rate of substitution between risk and return must be constant, i.e, IC will be linear.
As return is the commodity with positive marginal utility, IC closer to return axis gives higher level of satisfaction.
c. draw a set of indifference curves for a person that likes risk.
U^=U(r,s)
Totally differentiating both sides, we have,
0=MUmdm+MUsds
Or, dm/ds=-MUs/Mum>0
So, IC will be upward rising.
In this case, risk is still undesirable for the individual, but as he is risk lover marginal rate of substitution between risk and return must be increasing, i.e, IC will be convex to risk axis.
As return is the commodity with positive marginal utility, IC closer to return axis gives higher level of satisfaction.
2. You are the only European firm selling vacation trips to the North Pole. You
know only three customers are in the market. You offer two services, round trip
airfare and a stay at the Polar Bear Hotel. It costs you 300 euros to host a travele
at the Polar Bear and 300 euros for the airfare. If you do not bundle the services, a
customer might buy your airfare but not stay at the hotel. A customer could also
travel to the North Pole in some other way (by private plane), but still stay at the
Polar Bear. The customers have the following reservation prices for these
services:
a. If you do not bundle the hotel and airfare, what are the optimal prices PA and
PH, and what profits do you earn?
. If you only sell the hotel and airfare in a bundle, what is the optimal price of
the bundle PB, and what profits do you earn?
c. Could you do better (i.e. earn higher profits) by allowing your customers the
choice of purchasing airfares and hotel tickets separately or as bundle? If so,in
what are the optimal prices for the separate hotel, the separate airfare, and the
undle? This strategy is called "mixed bundling". We did not cover it in
lectures; see if you can work it out from first principles).
In case of both separate pricing options and mixed bundling, each person buys the commodity as long as price exceeds his willingness to pay.
We know that,
    
    willinnmess to pay
    
    customer
    airfare
    hotel
    total
    1
    100
    800
    900
    2
    500
    500
    1000
    3
    800
    100
    900
So, under single pricing options, he can charge either $500 or $800 for airfare and hotel room separately (since cost of both service is $300, he will never charge $100 as it will incur loss).
    pricing options under single pricing
    
    
    
    
    
    
    
    price
    no. of customers
    total cost
    profit
    airfare
    500
    2
    600
    (500*2)-600=400
    
    800
    1
    300
    500
    hotel
    500
    2
    600
    400
    
    800
    1
    300
    500
Thus, he will charge $800 for room rent and airfare individually and earn profit =$1000.
In case of mixed bundling, he can charge either $900 or $100.
    pricing option under bundling:
    
    price
    no. of customers
    total cost
    profit
    900
    3
    1800
    900
    1000
    1
    600
    400
So, his optimal strategy is to charge $900 and earn profit =$900.
Since single pricing option earns higher profit than mixed bundling, he will set separate prices for airfare and hotel room.
3. The Dill Corporation has a virtual monopoly in the ultra high speed compute
market. Dill has recently introduced a new computer that will be used by satellite
installations around the world. The installations have identical demands for the
computers. Dill's managers have decided to lease rather than sell the computer,
ut they have been unable to decide whether to use a single hourly rental charge
or a two-part tariff. Under the two-part tariff, users would be levied an "access
charge" plus an hourly rental rate. Dill's marketing staff estimates...