2 goods in economy : C - Consumption , L - Leisure

Given utility function:

u(L,C) = ln(L) + ln (C)

subject to budget constraint: C = wh - wL

where:

C is consumption, L is labor, w is wage rate, h is hours in a day (24hrs).

a. Form a mathematical formula for the indifference curve and draw it with L on the x-axis and C on the y-axis. Write down the slope of the indifference curve for any (L, C) and explain what it means.

b. Write down the slope of the budget constraint.

c. Then, maximize the above utility function using the Langrangian method with respect to (L,C) subject to the budget constraint. Compare your answers to (a) and (b) and explain.