Suppose is the number of left shoes and the number of right shoes. A consumer can only use pairs of shoes. Hence, his utility is .
In a cloud computing environment, there is a large server that runs many different tasks. Suppose a certain type of a task requires 2 CPUs, 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: .
A consumer with a Leontief utility function has the following properties:
The preferences are weakly monotone but not strictly monotone: having a larger quantity of a single good does not increase utility, but having a larger quantity of all goods does.
The preferences are weakly convex, but not strictly convex: a mix of two equivalent bundles may be either equivalent to or better than the original bundles.
The indifference curves are L-shaped and their corners are determined by the weights. E.g, for the function , the corners of the indifferent curves are at where .
The consumer's demand is always to get the goods in constant ratios determined by the weights, i.e. the consumer demands a bundle where is determined by the income: . Since the Marshallian demand function of every good is increasing in income, all goods are normal goods.
Since Leontief utilities are not strictly convex, they do not satisfy the requirements of the Arrow-Debreu model for existence of a competitive equilibrium. Indeed, a Leontief economy is not guaranteed to have a competitive equilibrium. There are restricted families of Leontief economies that do have a competitive equilibrium.
^ abCodenotti, Bruno; Saberi, Amin; Varadarajan, Kasturi; Ye, Yinyu (2006). "Leontief economies encode nonzero sum two-player games". Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06. p. 659. doi:10.1145/1109557.1109629. ISBN0898716055.
^Codenotti, Bruno; Varadarajan, Kasturi (2004). "Efficient Computation of Equilibrium Prices for Markets with Leontief Utilities". Automata, Languages and Programming. Lecture Notes in Computer Science. 3142. p. 371. doi:10.1007/978-3-540-27836-8_33. ISBN978-3-540-22849-3.
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