Consider a Consumer with Preferences for Consumption of a Composite

question 18

Essay

Consider a consumer with preferences for consumption of a composite good (C)and leisure (L)given by the following utility function:
U(C,L)= 2C^1/2 + L
Denote the consumer's wage rate by w and total time available for labor and leisure is normalized to one.The price of consumption is one.Denote the amount of labor supplied as N,so that
N + L = 1.The consumer also earns non-labor income ("allowance")of 0.
a.Write out the budget constraint determining feasible allocations of leisure and consumption.
b.Compute the optimal bundle of leisure and optimal bundle of consumption.
c.Derive the consumer's labor supply function: N*(w,).
d.Determine the effect of increasing non-labor income on the supply of labor (that is,compute the relevant partial derivative).
e.How does non-labor income affect the consumption of the composite good,C?
f.Compute the effects of an increase in wage on consumption and labor supply.Is leisure a normal good?

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Definitions:

Store Equipment

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Periodic Inventory Method

An accounting method where inventory is physically counted and valued at specific intervals.

Voucher Payment

Voucher payment involves the use of a voucher system where approval documents are prepared and used as the basis for making payments to vendors.

Net Method

An accounting practice where discounts for early payment are assumed to be taken and purchase or sale transactions are recorded at the net, discounted amount.