Problem $4.$ Suppose a flower shop has a monopoly in the market for a new type of

orchid, which no other flower shop is able to produce. Because this orchid is very rare,

every consumer$$s individual demand for these orchids is Q $=125-2$P$.$ There are $100$

consumers. The flower shop is able to produce the orchid at a marginal cost of $$25.$

Econ$440$: Problem Set #$43$

$1.$ Suppose that the owner simply decides how many orchids to produce. How many

are produced? How many does each consumer purchase? What is the market price

of an orchid? $(4$ points$)$

$2.$ What is the firm$$s profit? $(2$ points$)$

$3.$ Under this scenario, what is consumer surplus? $(2$ points$)$

$4.$ Suppose that instead the owner decides that it will expand the new flower$$s cachet

if only $$members$$ can purchase the orchids. The owner decides this is a risky

experiment and decides not to change the price of an orchid from the one specified

above. What is the highest price the owner can sell memberships? $(5$ points$)$

$5.$ Now, what are total profits of the firm? What is consumer surplus for each mem$-$

ber? $(2$ points$)$

$6.$ The owner is quite pleased with his membership program, but is surprised to

hear you suggest that he could make even more profit. He offers to give you the

difference in profits if you can do better than him. You propose a scheme which

will generate the maximum possible profit. What is the scheme? How much do

you make? $(5$ points$)$