There are two goods, coffee and mineral water, available in arbitrary nonnegative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function: u(c, m) = min{c, m} + c + m,
There are two goods, coffee and mineral water, available in arbitrary nonnegative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:
u(c, m) = min{c, m} + c + m,
where c is the quantity of coffee (in grams) and m is the quantity of mineral water (in liters).
The consumer has wealth in Dirhams of w > 0. The
Now assume that w = 100, p = 10 and q = 10. In addition to the monetary
budget constraint, the consumer has a time constraint. The consumer has
only 100 minutes available for the consumption of both goods. It takes
5 minutes/liter to consume water and and 20 minutes/gram to consume
coffee.
(a) In an appropriate diagram, illustrate the consumer’s constraint set. Your diagram should illustrate the monetary budget constraint, the time constraint, and indicate the consumer’s overall constraint set (i.e., the set of all consumption bundles the consumer can consume given their limited income and the prices of the goods, as well as the consumers limited time and the time it takes to consume each of the goods).
(b) Find the optimal consumption bundle and illustrate the solution in an appropriate diagram.
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