Home / Summaries / Managerial economics / product-price-quality

Product differentiation

Q: What is the problem of the monopolist for vertical differentiation?

Two profit-maximizing rules - Marginal revenue equals marginal cost on the last unit sold for given quality - Marginal revenue from increased quality equals marginal cost of increased quality for a given quantity p(Q,Z) = p = Z(theta - Q) MC(Q) = 0 C(Z) = alphaZ^2 dC/dZ = 2alphaZ pi(Q,Z) = Z(Theta-Q)Q-alphaZ^2 MR = Z*Theta - 2ZQ Q* = theta/2 p* = ZTheta/2 pQ = ZTheta^2/4 MR(Z) = Theta^2/4 MR = MC Givez Z* = Theta^2/(8alpha)

Q: How does Bertrand competition and the spatial model work?

How is x,m where the two lines cross, determined? X,m(p,1 , p,2) = (p,2 - p,1 + t)/2t D1 = N(p,2-p,1+t)/2t pi,1 = N(p,2p1-p,1^2+tp,1+cp,1-cp,2-ct)/2t Best response function for both shops are p1* = (p2+t+c)/2 p2* = (p1+t+c)/2 Which gives optimal price to be: p* = t+c for both and gives profit pi=Nt/2

Q: How do demand and quality relate?

Qi = 1 if p,i <= Ri(z) Qi = 0 if p,i > Ri(z) Each consumer buys one unit if price is lower than the reservation price, which is influenced by quality. Aggregrate demand is of the form: p = p(Q,z) Demand is a negative function of quantity Demand is a positive function of quality

8 important questions on Product differentiation

What is a spatial approach?

We need a model that describes differences in horizontal differentiation. The model describes a preference space, a measure of distance, and how costly it is to move away from your favorite product.

There is an incentive to find areas of the product space that are empty to place a product. Products should, however,
be kept at an optimal distance between each other to avoid cannibalization.

What is the hotelling model?

It is used to study:
Firms location: how many products and where in space
Firms price decision: how much to price each version

The model can also apply to space, time and product characteristics

What assumptions are made in the spatial approach in a monopolist case?

N consumers living equally spaced on a street which is 1 km long. Each consumer buys one unit of the product and has a valuation V for the product. Consumers incur there-and-back transport costs of t per mile. Marginal cost to produce the product is c. V is large enough so that v-c-t>0. Monopolist sets price to p,1. Overal cost for the product is p,1 + tx. A line in both directions. X,1 = (V-p)/t = max distance

What can we say about high/low transportation costs?

If transportation costs are high, then the solution is interior and the monopolist finds optimal to post a price that serves only part of the market

If transportations costs are low, then the solution is likely not to be interior and the monopolist serves the whole market, most likely at the price that makes indifferent the extreme consumers

How does a monopolist determine the amount of shops in a spatial model?

The monopolist faces a trade-off
- more shops allows to better cover the space
- opening one has a cost
We solve
pi(N,n+1) > pi(N,n)
n(n+1) < tN/2F

What is the problem of the monopolist for vertical differentiation?

Two profit-maximizing rules
- Marginal revenue equals marginal cost on the last unit sold for given quality
- Marginal revenue from increased quality equals marginal cost of increased quality for a given quantity

p(Q,Z) = p = Z(theta - Q)
MC(Q) = 0
C(Z) = alphaZ^2
dC/dZ = 2alphaZ

pi(Q,Z) = Z(Theta-Q)Q-alphaZ^2
MR = Z*Theta - 2ZQ
Q* = theta/2
p* = ZTheta/2

pQ = ZTheta^2/4
MR(Z) = Theta^2/4
MR = MC
Givez Z* = Theta^2/(8alpha)

How does Bertrand competition and the spatial model work?

How is x,m where the two lines cross, determined?
X,m(p,1 , p,2) = (p,2 - p,1 + t)/2t
D1 = N(p,2-p,1+t)/2t
pi,1 = N(p,2p1-p,1^2+tp,1+cp,1-cp,2-ct)/2t
Best response function for both shops are
p1* = (p2+t+c)/2
p2* = (p1+t+c)/2
Which gives optimal price to be: p* = t+c for both and gives profit pi=Nt/2

How do demand and quality relate?

Qi = 1 if p,i <= Ri(z)
Qi = 0 if p,i > Ri(z)
Each consumer buys one unit if price is lower than the reservation price, which is influenced by quality.

Aggregrate demand is of the form: p = p(Q,z)
Demand is a negative function of quantity
Demand is a positive function of quality

The question on the page originate from the summary of the following study material:

Managerial economics

View summary

A unique study and practice tool
Never study anything twice again
Get the grades you hope for
100% sure, 100% understanding

Remember faster, study better. Scientifically proven.

Product differentiation

8 important questions on Product differentiation

What is a spatial approach?

What is the hotelling model?

What assumptions are made in the spatial approach in a monopolist case?

What can we say about high/low transportation costs?

How does a monopolist determine the amount of shops in a spatial model?

What is the problem of the monopolist for vertical differentiation?

How does Bertrand competition and the spatial model work?

How do demand and quality relate?

Summaries related to Product differentiation

Managerial economics

Introduction to Law

Business Information Systems

Lineaire Optimalisatie

Principles of Database Management

Consumer Behaviour

Computer Netwerken

Architecture and Modelling of Management Inf…

ICT Service Management

Knowledge Management and Business Intelligen…

Management Control and Cost Management

Strategy