Ramirez, ECON 104, LMAT-A5.pdf

LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez ECONOMICS 104 Topic 5: Labor Supply & Time Allocation Model LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez LEARNING OBJECTIVES At the end of the topic, the learners should be able to: demonstrate ch...

LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez ECONOMICS 104 Topic 5: Labor Supply & Time Allocation Model LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez LEARNING OBJECTIVES At the end of the topic, the learners should be able to: demonstrate choice of optimal working time among labor owners analyze the dual effect response of workers to change in factor prices and how the labor supply curve is derived 1 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez TIME ALLOCATION MODEL Gary S. Becker A Theory of the Allocation of Time (1965) The decision to work is a result of optimal time allocation The decision of each individual (whether to spend his/her time working or for leisure), when pooled together, determines the labor supply curve LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez ASSUMPTIONS The individual can allocate his/her time for leisure and for working (labor) Work does not provide utility for the individual, leisure does The individual will be willing to work if compensated The individual derives utility from what he/she can consume from his/her income 2 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez ELEMENTS OF THE MODEL H – maximum amount of time available h – time spent on leisure L – time spent on work Thus, H  h  L Y  wL Y is the wage income Y  pC pC is total expenditure LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Utility Function: U  U h, C  Indifference Curve: U 0  U 0 h, C  C MU h MRShC  MU C U0 h diminishing MRShC 3 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Y Wage Income: Y  wL w0 L Y  pC pC  wL No savings Budget Constraint: H hL L  H h Y  w H  h Y wH - wh Maximum possible Value of forgone income due to income consumption of leisure LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Note: w – price of labor – opportunity cost of leisure pC  wH  wh wH  wh  pC Value of Value of goods Value of available time for consumption leisure time resource 4 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez wH  w  C    h   p p  variable intercept slope C wH wH max C  p slope   w p p max h  H since L  H  h C w h  H h p LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez CHOICE OF OPTIMAL WORKING TIME The individual chooses h = h* and C = C* which maximizes utility subject to the income (time) constraint max U  U h, C  s.t. wH  wh  pC Lagrangean Equation:  h, C,    U h, C    wH  wh  pC  5 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez FOCs for U-max  U 0  w  0 h h  U 0 p  0 C C   0  wH  wh  pC  0  Using the first two FOCs we have: U U h   w h  w MU h w  U  p U p MU C p C C LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez U-max condition w MRShC  p preferential rate of market rate of exchange of h for C exchange of h for C C w MRShC  p C* h* h h* L* 6 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Note: wH  wh *  pC * wL*  pC*  Y * w consumption is labor hours in L*  C * p real wage terms U *  U * h*, C * U *  U * H  L *, C * U depends on L negatively (on h positively) U depends on C positively LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Try this! Analyze the behavior of the individual in cases where MRShC  w p. Be sure to do the analysis mathematically, graphically and explain the rationale for such behavior. Try this! Solve for h*, L*, C* and U* Given: U  10h0.5C 0.5 w  10, p  5 Note: In the end, you can let H  24 to get specific values for your answers. 7 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez LABOR SUPPLY AND INPUT PRICE CHANGES What happens to labor supply when w changes? the opportunity cost of leisure time increases the value of the total time resource increases We can divide the effect of factor price changes to individual behavior (labor- leisure choice) into two parts: Substitution Effect Income Effect LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Substitution Effect Consider an increase in the wage rate from w to w’ w w' As w increases, p also rises to say, p The reward for working increases The opportunity cost of spending time on leisure increases The original combination  h0 , C0  is no w' longer utility-maximizing, i.e. MRShC 0  p 8  LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez The individual would allocate more time working and less time for leisure. w' Find MRShC  1 C p w' h0 h '  h  1 MRShC  slope   w' p p L0 L '  L  C0 C '  C  C’ B A w C0 0 MRShC  p h’ h0 h L’ L0 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Conclusion (via SE): h L C 0 0 0 w w w Recall: w MU h    MU h w  MRShC    MU C p p MU C   MU h  h  MU C  C by  L Homework: show SE for a decrease in the wage 9 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Income Effect Consider an increase in the wage rate from w to w’ increase in w will increase the value of total time resource, i.e. w ' H  wH Assumption: both C and h are normal goods, i.e. C h 0 0   wH    wH  Since h is a normal good, then as w increases, h increases (and L decreases) LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Conclusion (via IE): h  ( wH ) h 0 0 0  ( wH ) w w since L  H  h L 0 w Try this! show IE for a decrease in the wage 10 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Final/Net Effect Recall: SE: h L 0 0 w SE w SE IE: h L 0 0 w IE w IE FE = SE+IE: h h h  L L L    0   0 w FE w SE w IE  w FE w SE w IE  () () () () LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Note: Suppose the price of L (w) increases: C w' H p wH p H h 11 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Graphically: C SE :  h IE :  h since SE>IE, NE:  h C C2 B C1 A U’ C0 U h1 h2 h0 h SE IE FE LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Graphically: C SE :  L IE :  L since SE>IE, NE:  L C C2 B C1 A U’ C0 U L1 L2 L0 h SE IE FE 12 LMAT-A5 Learning Facilitator: Paul Joseph B. Ramirez Given varying magnitudes of SE and IE, how would the labor supply curve look like? w w = w(L) Backward-Bending Labor Supply Curve w = w(L) SE>IE w SEIE SE