Consider the market for coffee machines. There are 200 risk-neutral buyers and 160 risk-neutral sellers. Each buyer want
Posted: Sun Jun 05, 2022 3:51 pm
Consider the market for coffee machines. There are 200
risk-neutral buyers and 160 risk-neutral sellers. Each buyer wants
to buy at most one coffee machine; each seller owns exactly one
coffee machine.
There are two types of coffee machines: high quality and low
quality machines. High quality machines have a failure probability
of 0.2, whereas the low quality machines have a failure probability
of 0.75.
The utility that a buyer derives from a coffee machine without
failure amounts to 400 (measured in monetary terms). If the coffee
machine has a failure the utility of the buyer decreases – by the
amount of the repair costs – to 200.
Assume that 25% of the coffee machines are of high quality. Each
seller has a reservation price of 300 for a high quality machine
and a reservation price of 240 for a low quality machine.
a) Derive a buyer’s maximum willingness to pay for a high
quality and a low quality coffee machine.
Suppose that sellers know the quality of their machines, whereas
the buyers cannot distinguish between high and low quality machines
(asymmetric information).
b) Derive aggregate supply and aggregate demand as a function of
the market price.
c) Characterize the market outcome. Comment briefly on its
efficiency.
d) How large may the failure probability of the low quality
machines maximally be, so that there is just no partial market
breakdown
risk-neutral buyers and 160 risk-neutral sellers. Each buyer wants
to buy at most one coffee machine; each seller owns exactly one
coffee machine.
There are two types of coffee machines: high quality and low
quality machines. High quality machines have a failure probability
of 0.2, whereas the low quality machines have a failure probability
of 0.75.
The utility that a buyer derives from a coffee machine without
failure amounts to 400 (measured in monetary terms). If the coffee
machine has a failure the utility of the buyer decreases – by the
amount of the repair costs – to 200.
Assume that 25% of the coffee machines are of high quality. Each
seller has a reservation price of 300 for a high quality machine
and a reservation price of 240 for a low quality machine.
a) Derive a buyer’s maximum willingness to pay for a high
quality and a low quality coffee machine.
Suppose that sellers know the quality of their machines, whereas
the buyers cannot distinguish between high and low quality machines
(asymmetric information).
b) Derive aggregate supply and aggregate demand as a function of
the market price.
c) Characterize the market outcome. Comment briefly on its
efficiency.
d) How large may the failure probability of the low quality
machines maximally be, so that there is just no partial market
breakdown