Question

Consider a consumer that has preferences defined over bundles
of non-negative amounts of each of two commodities. The consumer’s
consumption set is R2+. Suppose that the consumer’s preferences can
be represented by a utility func- tion, U(x1,x2). We could imagine
a three dimensional graph in which the “base” axes are the quantity
of commodity one available to the consumer (q1) and the quantity of
commodity two available to the consumer (q2) respec- tively. The
third axis will be the “height” axis. This will represent the value
taken by the utility function at each combination of q1 and q2. An
indiffer- ence curve map for this consumer is essentially the view
that you would get of this graph if you were looking down on it
from directly above, so that your line of sight is parallel with
the “utility” axis. It will be a two-dimensional diagram that looks
like a topographical map that people might use when they are
hiking. The indifference curves play the role of contour lines.
They indicate the locus of commodity bundles that yield the same
utility level. Explain why it might be a good idea to indicate the
direction (or directions) in which utility is increasing on the
consumer’s indifference curve map.

Answer #1

Suppose that a consumer has perfect complements, or Leontief,
preferences over bundles of non-negative amounts of each of two
commodities. The consumer’s consumption set is R^2(positive). The
consumer’s preferences can be represented by a utility function of
the form U(x1, x2) = min(x1, x2).
1. Illustrate the consumer’s weak preference set for an
arbitrary (but fixed) utility level U.
2. Illustrate a representative iso-expenditure line for the
consumer.
3. Illustrate the consumer’s utility-constrained expenditure
minimisation problem.
4. Illustrate the derivation...

Suppose that a consumer has preferences over bundles of
non-negative amounts of each two goods, x1 and x2, that can be
represented by a quasi-linear utility
function of the form
U(x1,x2)=x1 +√x2.
The consumer is a price taker who faces a price per unit of good
one that is equal to $p1 and a price per unit of good two that is
equal to $p2. An- swer each of the following questions. To keep
things relatively simple, focus only on...

Total utility can be objectively measured in numbers that
indicate usefulness or benefit to the consumer.
____ 2. Consumers should purchase quantities of a good to the
point where MU > P.
____ 3. Voluntary exchange requires that there must be mutual
gain.
____ 4. Points along a budget line represent the maximum
combinations of two commodities that a consumer can afford.
____ 5. The budget line represents a consumer's preferences
for a commodity.
____ 6. A change in consumer...

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