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Exercises · Q24
Q.

The following table gives the marginal product schedule of labour. It is also given that total product of labour is zero at zero level of employment. Calculate the total and average product schedules of labour.

LLMPLMP_L
13
25
37
45
53
61
Goa GbshseTextbookSubjective· 3mImportance★★★★★
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Total product is the cumulative sum of marginal products, and average product is total product divided by labour. Starting from zero, we add each MPLMP_L to get TPTP, then divide by LL to get APAP.

The marginal product of labour (MPLMP_L) tells us the additional output produced when one more unit of labour is employed. If you know the total product at zero employment is zero, then each subsequent MPLMP_L simply adds to the running total. This is the fundamental relationship:

TP(L)=TP(L−1)+MPL(L)TP(L) = TP(L-1) + MP_L(L)

AP(L)=TP(L)LAP(L) = \frac{TP(L)}{L}

Let’s build the table step by step.

Step 1: Total product from marginal product

  • At L=0L=0, TP=0TP = 0 (given).
  • At L=1L=1, MP=3MP = 3, so TP=0+3=3TP = 0 + 3 = 3.
  • At L=2L=2, MP=5MP = 5, so TP=3+5=8TP = 3 + 5 = 8.
  • At L=3L=3, MP=7MP = 7, so TP=8+7=15TP = 8 + 7 = 15.
  • At L=4L=4, MP=5MP = 5, so TP=15+5=20TP = 15 + 5 = 20.
  • At L=5L=5, MP=3MP = 3, so TP=20+3=23TP = 20 + 3 = 23.
  • At L=6L=6, MP=1MP = 1, so TP=23+1=24TP = 23 + 1 = 24.

Step 2: Average product from total product

Average product is simply TPTP divided by LL:

  • L=1L=1: AP=3/1=3AP = 3/1 = 3
  • L=2L=2: AP=8/2=4AP = 8/2 = 4
  • L=3L=3: AP=15/3=5AP = 15/3 = 5
  • L=4L=4: AP=20/4=5AP = 20/4 = 5
  • L=5L=5: AP=23/5=4.6AP = 23/5 = 4.6
  • L=6L=6: AP=24/6=4AP = 24/6 = 4 …

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