Problem One (40 Marks) Assume Zoe’s utility function is U(C. L)-C * L where C s consumption measured by her total income and L is leisure. Total income is labour income and non-labour income. She has y $400 on-labour income and a total of 150 hours to allocate between work (consumption) and leisure at the market wage ree of w = $10 per hour. a) Write down the budget constraint and the slope of the badget constraint. (2 marks) b) Solve the optimal desired hours of leisure (L) and work (h). (2 marks) e) Calculate the quantity of utility, (1 mark) Draw Zoë’s budget constraint and indifference curve. Label the horizontal and vertical intercepts and optimal leisure and coesumption quantities. (2 marks) Suppose a company makes a job offer to Zoè However, this company needs to design a system that motivates her to work more hours The following two seenarios are suggested Scenario 1) Straight-time equivalent( 17 marks) Suppose the company increases the hourly wage to w = $ 16 per hour. c) Solve the new optimal kisure work choice (L and ). (2 marks) Draw a new graph and show the income, substitution and total effects on your graph. Label all the necessary details. (4 marks) g) Calculate the size of the income and substitution effects (IE&SE) for hours of work (h).(Hint:You can solve this by setning np thwo equarions: . Use the opimal condition thar gives the relation between C and L (call them C and Ll 2. The wtality amoant from C2 and L2 needs to be egual to the original unilary in part e. Subntiuein 2 and solve C2 and L2 Then,yow ean ase them to calealate lE and SE) (4 marks) (3 marks) h) Calculate the uncompensated, compensated and income elasticities of labor gpply )Bricfy espinin whether leisure is a normal or inferior good. (2 marks) Fill in the blanks. Zoe’s labour supply curve has a (negative, positive, vertical) slope because the substitution effect is (larger han, equal to smaller than) the income effect. (2 marks) Scenario II Overtime premium (16 marks) Suppose the job offer requires her to work = 70 hours per month at $10/h and double pay for every hour beyond 70. The ahemative, for her, is not to work at all. k) Show that Zoé is better off accepting the offer than the alternative. (2 marks 1) Write down the new budget constrains knowing that the 70 hours of work is mandatory Hin The hudget line is kinked so yow need to define two parts.An equarion for hours of wonk up to 70 and an eyaation for hours of work ahove 70)(2 marks) m) Find the optimal hours of work after accepting the offer. (Hint: Given that the offer is accepted you should find how mawy hours of the remaining available time (150-70-80) is allocated between work and eisure. Then, you canw caculale the total hours of wonk and leiswre) 43 marks) n) Use the appropriate budget constraint and indifference curves and show the following on one graph.(4 marks) a The optimal point in the original case. b. The offered hours in scenario II. c. The optimal choice in scerario B (less than, more than, equal to) the Fill in the blank. In scenario ll. Zoe chooses to work mandatory hours, because leisure is(more, less, oqually) expensive and the income effect is o) (larger than, equal to, smaller than) the substitution effect. (3 marks p) Compare the two scenarios and brigty, explain which scenario suits the compamy’s meeds better? Is this also the preferred scenario for Zoe? (2 marks)
The post Question: Problem One (40 Marks) Assume Zoe’s utility function is U(C. L)-C * L appeared first on WriteDen.
Source: my posts
