Question

In: Economics

24 hours a day, there are workers who use 16 hours of leisure (L) and labor...

24 hours a day, there are workers who use 16 hours of leisure (L) and labor (E), excluding 8 hours of sleep. It benefits from the workers' leisure (L) and consumption (C). The utility function of this worker is U(L, C)=L*C. The worker's hourly wage is 10 and the given non-earned income is 10. When both labor and capital income are used for consumption (C), find consumption C that maximizes utility of workers. (However, the price of consumer goods is 1)

Solutions

Expert Solution

Price of consumption, Pc = 1
Price of leisure, Pl = wage = 10
Slope of budget constraint = Pl/Pc = 10/1 = 10

MRS = MUL/MUC = (dU/dL)/(dU/dC) = C/L

So, utility is maximized when MRS = slope of budget constraint
Thus, C/L = 10
So, C = 10L

Total income = total income from working + non-earned income = (16*10) + 10 = 160 + 10 = 170

Budget constraint: Pl*L + Pc*C = total income
So, 10L + 1C = 170
So, 10L + 10L = 20L = 170
So, L = 170/20
So, L = 8.5

C = 10L = 10*(8.5)
Thus, C = 85

Rahul Sunny answered 2 years ago
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