Microeconomics- Labour supply, overtime wage

Reply Mon 30 Oct, 2017 08:17 am
Ron has 75 hours a week which he can allocate between work (L) or leisure (R). Suppose that if he 
works he receives a wage rate of 4 euros and hour, and that the other good that provides him 
with utility is consumption spending (C), measured in euros. 
(a) Draw Ron’s budget line, putting R on the horizontal axis and C on the vertical axis, and being 
careful to label axes and the points at which the budget line intersects the axes.  
(b) Now suppose that Ron’s employer introduces an overtime payment of 1.5 times the normal 
wage rate for hours in excess of 40 hours of work per week. Add this overtime payment to 
your diagram, in order to show how it modifies Ron’s budget constraint. Be careful to label 
the new part of the budget line, and any new intercepts with the axes.  
(c) Suppose that before the introduction of the overtime payment, Ron was rationally choosing 
to work 45 hours a week. What can we say about whether he will work for more or fewer 
hours with the overtime pay?  
Explain your answer in terms of the income and substitution effects of the introduction of 
the overtime pay, supposing that leisure is a normal good. You may use diagrams if you 

My problem is with question (c), I don't get how substitute effect and income effect work here.
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Reply Wed 8 Nov, 2017 04:41 pm
First, you need to consider that the orizontal intercept is always 75, because that is the maximum amount of hours that Ron can dedicate to leisure.

When the wage is 4, the vertical intercept is (75-0)*4, and it measures both the Income and the consumption of composite good (whose price is €1).

Since there is only one line passing for two points, you can now draw the budget line.

B) The employer applies a wage of €6 per hour in excess of 40 hours (4*1.5=6)
If Ron works for more that 40 hours, then he can dedicate less that 35 hours a week to leisure (75-40= 35). Thus, I think I'd use the budget line corresponding to a wage of 6 from 0 to 35 hours of leisure (Y-intercept is 75*6=450), I'd draw a vertical red line and from 36 to 75 I'd use the budget line corresponding to a wage of 4, because if Ron dedicates more than 35 hours to leisure, he'll never get over 40 hours of work per week.

C) Initially Ron used to rationally choose 45h a week of work. You can't state anything for certain here, since you don't have any informations about Ron's preferences, but generally when we talk about work offer I can state for sure that over a certain level of w (wage), the work offer decreases.

If you draw an indifference curve with a tangency point at 45 on the first budget line (wage = 4), than you know that the slope of the budget line is equal to |px/py|, which is |w/1|, = |w| (= abs(w)). When the slope of the budget line increases from 4 to 6, than you can figure out that the tangency point moves to an higher point on the same indifference curve.

To understand now how the substitution effect and the income effect work here, you have first to remember how they're defined.

The substitution effect is the change in demand of a good needed when its price changes, to reach the initial level of Utility (= same indifference curve).

The income effect is the change in demand of a good when its price changes, due to the change in the purchasing power of his income.

(When the income increases, the budget line moves in parallel).

To find the effects graphically,
• draw the first budget line (w = 4)
• draw the second budget line (w = 6)
• draw a point (A) having coordinates (30, 120) which lays on the first budget line
• draw a point (B) corresponding the the tangency point between the new budget line and the higher indifference curve (I guess you can just draw them randomly here)
• To find the intermediate basket (C) you need to move the 2nd budget line back in parallel until you get a tangency point between this line you're moving and the initial indifference curve.
• Xc-Xa = substitution effect
• Xb-Xc = Income effect

• Here the income effect is of course positive, because the increase in the wage leads Ron to increase the hours of work (if you think, you wouldn't be willing to work for €0.10 per hour, but you would for €15, for instance)
• The substitution effect is instead negative, because now, with an higher wage, it takes less hours of work to get the same basket as before, and to be able to afford the same basket you have to work less.

If the substitution effect is higher than the income effect, you have in the end a decrease in the work supply. The substitution effects makes the optimal basket move left from Xa to Xb, and the income effect makes it move from Xb to Xc (Xb is left, Xa in right and Xb in the middle).

That's why the work supply decreases when the wage increases.
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Reply Wed 8 Nov, 2017 05:11 pm

This is my drawing, this way it should be easier for you.

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Reply Sat 2 Dec, 2017 01:21 pm
The overtime portion doesn't kick in until 40 hours of work at the regular slope.


(c) What can we say about how this will effect Ron's preferred work habit?
Ron's preference becomes the line segment between continuing to work 45 hours with additional consumption and maintaining the same level of consumption with additional recreational hours.
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