A monopolist with the constant marginal cost of 4 (MC ¡ 4) to just two consumer types, which are of equal size n. Members of group 1 have an individual inverse demand curve given by p1(q) = 16- 1 2 q while members of group 2 have individual inverse demand given by p2(q) = 20 - 1 2 q. (Because marginal cost is constant, you may assume each group has just one member.) Resale of the good among consumers is impossible. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
(1) Suppose the monopolist offers just a single two-part tariff. Calculate the one that maximizes its profit. Calculate the associated profit.
(2) Suppose the monopolist can not tell whether a person is in group 1 or group 2. So it offers a pair of two-part tariffs and lets each consumer buy according to the one he or she prefers. Calculate the profit-maximizing pair of two-part tariffs for the monopolist to offer. Calculate the associated profit.
(3) Suppose the monopolist offers just a single package for sale, described as (q0, T E0). Accordingly, a consumer has the choice of buying nothing or buying exactly q0 units for an item of total expenditure (payment from that consumer) of T E0. Determine the profit-maximizing single package to offer. How does this profit compare with that in the two previous parts?
(4) Suppose the monopolist offers two packages for sale, described as (q1, T E1) and (q2, T E2). Accordingly, a consumer has the choice of buying nothing or buying exactly q1 units for a total expenditure of T E1 or buying exactly q2 units for a total expenditure of T E2. (The monopolist envisions that those in group 1 will choose (q1, T E1) and those in group 2 will choose (q2, T E2).) Determine the profit-maximizing pair of packages to offer. Calculate the associated profit.
A monopolist with the constant marginal cost of 4 (MC ¡ 4) to just two consumer types, which are of equal size n. Members of group 1 have an individual inverse demand curve given by p1(q) = 16- 1 2 q while members of group 2 have individual inverse demand given by p2(q) = 20 - 1 2 q. (Because marginal cost is constant, you may assume each group has just one member.) Resale of the good among consumers is impossible. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
(1) Suppose the monopolist offers just a single two-part tariff. Calculate the one that maximizes its profit. Calculate the associated profit.
(2) Suppose the monopolist can not tell whether a person is in group 1 or group 2. So it offers a pair of two-part tariffs and lets each consumer buy according to the one he or she prefers. Calculate the profit-maximizing pair of two-part tariffs for the monopolist to offer. Calculate the associated profit.
(3) Suppose the monopolist offers just a single package for sale, described as (q0, T E0). Accordingly, a consumer has the choice of buying nothing or buying exactly q0 units for an item of total expenditure (payment from that consumer) of T E0. Determine the profit-maximizing single package to offer. How does this profit compare with that in the two previous parts?
(4) Suppose the monopolist offers two packages for sale, described as (q1, T E1) and (q2, T E2). Accordingly, a consumer has the choice of buying nothing or buying exactly q1 units for a total expenditure of T E1 or buying exactly q2 units for a total expenditure of T E2. (The monopolist envisions that those in group 1 will choose (q1, T E1) and those in group 2 will choose (q2, T E2).) Determine the profit-maximizing pair of packages to offer. Calculate the associated profit.
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Related questions
For Each of the following observations, check to see if the choices satisfy the Weak Axiom of Revealed Preference (WARP). If it does satisfy WARP, give as much information about the consumer's ranking of the bundles as possible. If it violates WARP, simply write It violates WARP.
a)
|
Observation |
PX |
PY |
X |
Y |
|
1 |
3 |
1 |
2 |
4 |
|
2 |
1 |
4 |
4 |
1 |
|
3 |
3 |
2 |
2 |
3 |
b)
|
Observation |
PX |
PY |
X |
Y |
|
1 |
1 |
5 |
3 |
2 |
|
2 |
3 |
2 |
2 |
1 |
|
3 |
2 |
4 |
1 |
4 |
2. Suppose there are two types of consumers. The demand for each type of consumer is given by:
Type A: Q = 70 - 2P
Type B: Q = 60 - 3P
Suppose a monopolist has constant marginal cost = 6. Also, for parts a-b, assume that the monopolist is unable to distinguish between the two types of consumers.
a) (4 points) What price should the monopolist charge?
b) (2 points) How much profit will this monopolist make?
Now suppose the monopolist is able to distinguish between the two types of consumers and can effectively price discriminate between them.
c) (4 points) What price should the monopolist charge to each type of consumer?
Price to type A consumers:
Price to type B consumers:
d) (4 points)How much total profit does the price discriminating monopolist make?
e) (2 points) Calculate the price elasticity of demand for Type A consumers at the monopolistâs profit maximizing price.
f) ) (2 points) Calculate the price elasticity of demand for Type B consumers at the monopolistâs profit maximizing price.
