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.
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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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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Step 1: State the given information
VIEWStep 2: Find Tom's budget constraint and find minimum & maximum value
VIEWStep 3: Draw Tom's budget
VIEWStep 4: Set up maximization problem, calculate consumption demand and leisure
VIEWStep 5: Find L* and C* using the given information in the question
VIEWStep 6: Analyze supply function of labor
VIEWStep 7: Find Tom's working hours without bursary
VIEWStep 8: Show the optimum
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