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sgillespie006p3ute8
sgillespie006p3ute8
25.02.2020 • 
Business

Exercise 3. Labor Supply (Cobb-Douglas) Each day you are endowed with 24 hours of time (T=24) that you can either spend working (L) or in leisure (l), so that T = L + l. The reason for working is so that you can earn an hourly income, w, and afford consumption of good, c. Assume that the price of the consumption good is normalized to one (p=1), so that your consumption is constrained by your wage income: c= WL a) You value both consumption, c, and leisure, l, and each day you cannot do without either one. Your daily utility is u =cl2. What is the MRS between consumption and leisure? b) Since your time constraint is T = L +l, then L=T-l. And since your budget constraint is CE WL, then c = w(T-). Rearranging you have c + wl = wł. The price of consumption is 1, the price of leisure is w, and the value of your time endowment is WT. Can you derive the labor supply? c) When the wage rate is w=10, what is c, l, and L? When the wage rate is w'=20, what is c', l', and L? When the wage rate is w"=30, what is c", l", and L"? d) In a graph with leisure on the horizontal axis, and consumption in the vertical axis, draw the budget constraint as it changes is w, w' and w", and label the three optimal bundles (c, ) that you found in part c. e) As the wage rate changes from w=10 to w'=20, can separate the substitution and endowment income effect for leisure?

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