Question 6 Consider the static labor supply model discussed in class, 1 and assu

Question

Question 6 Consider the static labor supply model discussed in class, 1 and assume U(c, l) = C^ 0.2 l ^(0.8). A worker chooses his level of labor supply and consumption according to the following maximization problem:1 maxU(c, l) = c^0.2 × l^0.8 , s.t. C wh + Y, h = 18 l, C, l 0

a) Assume that non-labor income Y = 100$ and that the wage rate is w = 10$/hour. Find the individual’s optimal level of labor supply (h) and his optimal level of consumption (c).

b) What happens if the wage increases to w = 12? Find the effect of a change in wage on labor supply.

c) Can you tell whether a worker will supply a larger number of hours when his wage goes up?

d) For this individual, which effect is larger when the wage increases: The income effect or the substitution effect?

e) Find the effect of a change in non-labor income Y on labor supply.

f) Find the worker’s reservation wage.

Explanation / Answer

an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent. That is, the consumer has no preference for one combination or bundle of goods over a different combination on the same curve. One can also refer to each point on the indifference curve as rendering the same level of utility (satisfaction) for the consumer. In other words, an indifference curve is the locus of various points showing different combinations of two goods providing equal utility to the consumer. Utility is then a device to represent preferences rather than something from which preferences come.[1] The main use of indifference curves is in the representation of potentially observable demand patterns for individual consumers over commodity bundles.[2]

There are infinitely many indifference curves: one passes through each combination. A collection of (selected) indifference curves, illustrated graphically, is referred to as an indifference map.

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