Joe can allocate his time between working and leisure. He earns a wage of $w per hour which he spends on consumption. His utility depends on leisure and consumption. The question asks to: (1) find Joe's optimal choice of work and leisure, (2) show how this changes with a wage cut using indifference curves, and (3) explain the substitution and income effects in terms of elasticities. It also asks to draw Joe's labor supply curve.

1. Joe can allocate his time
between working
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Joe can allocate his time between working
Joe can allocate his time between working (H – hours worked) and leisure (L – hours spentin leisure),and spends all
24 hours per day doing one or the other. He earns a wage of w dollars per hour, which he spends entirelyon
consumption ofall other goods (notincluding leisure time);he has no other source of income.Since we assume all
goods are measured in dollar amounts,consuming Ydollars’ worth of goods is ata price of $1 – it costs $1 to buy $1
worth of all goods.
His utility function is U= 3LY where Y is his total income.His =3 and his = 3.
a. [3 points]What levels of H and L does he choose in optimal? [Hint:optimalityhas to ensure 3 conditions here:
budgetconstraint,time constraintand the tangency condition]
b. [4 points]Now suppose Joe’s industrygoes into a rough phase and his boss has to slash Joe’s wages to μ. Draw a
diagram with leisure on the horizontal axis and all other goods on the vertical axis and the usual downward sloping
indifference curve. Show i) the budgetlines and the optimal choices for the two cases ofbefore and after the wage
cut (2 points) ii) the substitution effectand income effectfollowing the wage cut (2 points).[Hint: the expression from
part b should tell you where the optimal pointwill be on the new budgetline]
c. [2 points]Briefly explain the substitution effectand income effect situation from partb with special reference to the
income elasticityof leisure demand and the price elasticityof leisure demand.
d. [1 point]Draw Joe’s labour supplycurve using the information from parts a and c.
Please typewrite your answers.You should attemptto draw the graphs in MSWord or similar word processing
software.Label your graphs.If you absolutelycannotdraw graphs in software you can draw them by hand,ensure
they are very clear,take a photo/scan and insertthem in your MSWord file. Writing all of the assignmentbyhand and
scanning itin is not appreciated – you should atleasttype in your non-graph parts of the answers.
Save a copy of your assignmentas a backup.
Convert your assignmentinto a pdf file and upload them in the Assessments > Week 5> Online Short Answer link on
LMS. You can submitonlyonce, so go over your work thoroughly before you pdf it and upload it.
a. [3 points]
Full creditwill be given for showing all the steps for the calculations.0.5 pointwill be deducted if the final answer is
incorrectbut the steps were correct; 0.5 point will be deducted per incorrectstep but follow-through points will be
given.
b. [4 points]the budgetconstraint,indifference curve and the time constraint,that shows actual values ofJoe’s
optimal choice
Full creditwill be given if properly labelled budgetconstraints,time constraintand ICs are drawn indicating the
optimal choices.0.5 pointwill be deducted if some labels are missing or ifthe budget/time constraintis incorrector if
the optimal choice is notcorrectly indicated or if the IC is incorrect.

2. 1 pointfor correctly showing the SE including the direction of movementand 1 for correctly showing IE including the
direction of movement.
c. [2 points]
0.5 for correctly mentioning income elasticity,0.5 for correctly mentioning price elasticityand 1 point for tying up the
IE-SE logic with these elasticities.
d. [1 point]S of leisure.
0.5 will be deducted if labels are missing or if the S curve is incorrectly drawn.
Rubric:
• Name:Online ShortAnswer 2 – Levels of Achievement Rubric
• Description:This chartshows you the strengths and weaknesses ofyour attempt.
• Rubric Detail:Levels of Achievement
Items Weak CompetentProficient
Part a 0 to 1 point
Has very little idea how to calculate optimal consumption point.1 to 2 points
Did the calculations butmade major mistakes 2 to 3 points
Correct method ofcalculating optimal consumption point;possiblycalculation and minor mistakes,ifany.
Part b 0 to 1 points
Has very little idea of how to draw the graph and has not grasped conceptofprice effect decomposition.1 to 3 point
Drew the graphs and showed the price effect decomposition butthere were some major mistakes 3 to 4 points
Properly labelled graph showing SE and IE with minor mistakes,ifany.
Part c 0 to 0.5 point
Has very little idea of price decomposition and elasticityconcepts 0.5 to 1 points
Explanation in the rightdirection but weak. 1 to 2 points
Strong explanation;minor mistakes possibly,if any.
Part d 0 to 0 point
Has no idea of how to draw the graph 0 to 0.5 point
Drew the graph but there were some minor mistakes.0.5 to 1 point
Perfectly labelled and correctgraph