Woody lives in Houston, and works at a college restaurant where the minimum wage per hour, w, is paid. The current minimum wage rate per hour is $8. Woody allocates his daily hours either for working or for leisure. That is, for the total 24 hours he has a day, he can choose to work (denoted as H), or do other things (denoted as L). If he works, all the money he earns, w x H, is spent on his consumption. Saving is not poosible. Both consumption and leisure are goods for him.
Woody's utility function is
U(L,C)= Squre root of CL2
MUC=L/(2*Square root of C)
MUL=Sqaure root of C
a) Derive Woody's MRS function. What is the MRS at (L,C) = (20,32)? State the meaning of MRS in terms of leisure and consumption.
b) Derive Woody's budget constraint equation. (Hint: C=w x H, and the total hours a day is 24)
c) What is Woody's optimal (L*,C*) and utility level U*? How many hours does Woody work each day? Clearly state the utility maximization condition.
Woody lives in Houston, and works at a college restaurant where the minimum wage per hour, w, is paid. The current minimum wage rate per hour is $8. Woody allocates his daily hours either for working or for leisure. That is, for the total 24 hours he has a day, he can choose to work (denoted as H), or do other things (denoted as L). If he works, all the money he earns, w x H, is spent on his consumption. Saving is not poosible. Both consumption and leisure are goods for him.
Woody's utility function is
U(L,C)= Squre root of CL2
MUC=L/(2*Square root of C)
MUL=Sqaure root of C
a) Derive Woody's MRS function. What is the MRS at (L,C) = (20,32)? State the meaning of MRS in terms of leisure and consumption.
b) Derive Woody's budget constraint equation. (Hint: C=w x H, and the total hours a day is 24)
c) What is Woody's optimal (L*,C*) and utility level U*? How many hours does Woody work each day? Clearly state the utility maximization condition.
