The solutions are provided, explain each step carefully and what question the response is corresponding to$.$ Consider the simple model of consumer choice developed in class. The

consumer

is endowed with $h$ units of time which can be allocated to work and leisure. The budget

constraint for the consumer is $C=w{N}^s+-T.$

a$.$ Suppose Under standard preferences, show in a diagram the optimal

bundle for the consumer $($assume that optimal consumption is greater than $0).$

Explain why such a bundle is optimal and state two conditions that must be

satisfied by the optimal bundle.

b$.$ Suppose that preferences for the consumer are described by the utility function

$U=C^{}*l^{l-},$ where $$ is between $0$ and $1.$ Further suppose that $-T=0.$

Characterize the optimal consumer bundle and then illustrate it in a diagram. In

the same diagram, illustrate how the consumer's optimal bundle changes when the

real wage increases. Which dominates, the income effect or the substitution effect

$($or neither$)?$ Finally, characterize the consumer's optimal supply of labor and

illustrate it in a new diagram $($a labor supply curve$).(1)$ a$)C$

IF so consumer wANTS

To reduce $l.$ If $l>C^{**}=(h-l)+-TMR{S}_{lC}=l,Mrslc>$

$-(i)C^{**}=(h-l)+-T$

$(ii)MR{S}_{lC}=$