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You need to decide how many hours should Bob spend at work.

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Please solve 1-4

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Problem 3:
You need to decide how many hours should Bob spend at work. His total
available time is 24h and he has no income rather than salary. His current wage
is $100 per hour and he only consumes apples which cost $5 per pound.

1. What is Bob’s real wage (wage rate in terms of apples)?
2. Show Bob’s budget set on the graph.
3. Denote by R Bob’s leisure and by C his consumption. His utility function
is U(R, C) = R · C. What is his optimal time spent at work, his leisure
time and his consumption of apples?
4. Assume a wage increase to $200. Is there any change in Bob’s labor supply
(you have to calculate it)? Why?

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