Question 1 Tom is trying to figure out how to supplement his student bursary of £200 per week. He is considering a part-time job at a restaurant. The wage is £8 per hour. His utility function is U(C, L) = C L where C is his consumption measured in £ per week and L his leisure, measured in hours per week. The amount of leisure time that he has left after allowing for necessary academic activities is 50 hours a week. 1. Write out Tom's budget constraint and calculate the maximum value (i.e. he works the maximum time available) and minimum value? 2. Using your results from part 1, draw Tom's budget set (horizontal axis: leisure and vertical axis: consumption). 3. Let Y= student bursary, T = total amount of leisure time and w=wage. Set up the maximisation problem and calculate optimal consumption demand and leisure as a function of his student bursary and wage.
Question 1
Tom is trying to figure out how to supplement his student bursary of £200 per week. He is considering a part-time job at a restaurant. The wage is £8 per hour. His utility function is U(C, L) = C L where C is his consumption measured in £ per week and L his leisure, measured in hours per week. The amount of leisure time that he has left after allowing for necessary academic activities is 50 hours a week.
1. Write out Tom's budget constraint and calculate the maximum value (i.e. he works the maximum time available) and minimum value?
2. Using your results from part 1, draw Tom's budget set (horizontal axis: leisure and vertical axis: consumption).
3. Let Y= student bursary, T = total amount of leisure time and w=wage. Set up the maximisation problem and calculate optimal consumption demand and leisure as a function of his student bursary and wage.
4. For the values given in the question, work out the value for optimal leisure hours and consumption spending L* and C*.
5. Express his supply function for labour as a function of student bursary and wage. Is this backward bending? Justify your answer mathematically.
6. How many hours would Tom work if he did not receive any student bursary?
7. Show the optimum diagrammatically.
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