The Democratic People's Republic of Gruberland has two workers in its economy: worker A and worker B. Workers choose a combination of leisure and consumption to maximize their utility. The individual utility functions are as follows:

UA=C^7/8xZ^1/8

UB=C^1/2+(30Z)^1/2

whereC stands for consumption, andZ stands for leisure. Any given worker is constrained by a maximum of24 hours of leisure, or a maximum of24 hours spent working for an hourly wage,w. One unit of consumption costs $1.

Find the expression for the individual labor supply functions,LA(w)andLB(w) for each worker. To demonstrate that you have found the correct labor supply functions, solve for the labor supplies ifw=10

.

LA(10)=

LB(10)=

What is the aggregate labor supply in this economy?

L(10)=