Question

Assume that a worker has the Utility Function U(C,L) = C ^0.25​ ​ L^0.75​

“C” refers to consumption in dollars and “L” to hours of leisure in a day. The worker has an offered wage of $10 per hour, 20 hours available for leisure or work per day, and $90 dollars a day from non-labour income.

a)     ​ Find the budget constraint equation of the individual._​                  

b)    ​ Find the optimal choice for the individual in terms of units of leisure and income,_​                        the number of hours worked and the utility obtained.

c)     ​ Make a well labeled graph that illustrates the solution to the problem of the worker._​                                                                                                                                                                                                                 

d)    ​ Find the supply equation of the individual._​          

e)     ​ Calculate the reservation wage and briefly explain the definition._​

Answer 1

a)Budget constraint equation:

Consumption depends on income

C =wh+90

In this equation w is wage and h is hour that available for work or leisure.

For calculating income we should found the working hours. If we subtract leisure time we will get working hours .

C= 10(20-L)+90

C= 200-10L+90

C+10L=290------------------------------} Budget constraint equation

b) for Optimal choice

d)supply equation