economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...

, especially in consumer theory, a Leontief utility function is a function of the form:

u(x_1,\ldots,x_m)=\min\left\ .

where: *

m

is the number of different

goods In economics, goods are items that satisfy human wants and provide utility, for example, to a consumer making a purchase of a satisfying product. A common distinction is made between goods which are transferable, and services, which are not ...

in the economy. *

x_i

(for

i\in 1,\dots,m

) is the amount of good

i

in the bundle. *

w_i

(for

i\in 1,\dots,m

) is the weight of good

i

for the consumer. This form of utility function was first conceptualized by

Wassily Leontief Wassily Wassilyevich Leontief (russian: Васи́лий Васи́льевич Лео́нтьев; August 5, 1905 – February 5, 1999), was a Soviet-American economist known for his research on input–output analysis and how changes in one ...

Examples

Leontief utility functions represent complementary goods. For example: * Suppose

x_1

is the number of left shoes and

x_2

the number of right shoes. A consumer can only use pairs of shoes. Hence, his utility is

\min(x_1,x_2)

. * In a

cloud computing Cloud computing is the on-demand availability of computer system resources, especially data storage ( cloud storage) and computing power, without direct active management by the user. Large clouds often have functions distributed over m ...

environment, there is a large server that runs many different tasks. Suppose a certain type of a task requires 2

CPU A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, and ...

s, 3 gigabytes of memory and 4 gigabytes of disk-space to complete. The utility of the user is equal to the number of completed tasks. Hence, it can be represented by:

\min(, , )

Properties

A consumer with a Leontief utility function has the following properties: * The preferences are weakly monotone but not s