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#### Consider a farmer with the production function Y=10(I1/2)

###### Economics

Consider a farmer with the production function Y=10(I1/2).  Where Y is the quantity of corn produced and I is corn planted (I'm calling it I for "Investment").  So in each period, the farmer plants some amount (I) and then harvests the quantity given by Y.  Now let's imagine that each period the farmer consumes half of the output and plants the other half in the next period.  Finally, let's assume that the farmer starts by planting one unit.  Then let's see how output evolves over time.  I will get you started.  (t represents the time period.)

t                               I                                      Y

0                             1                                     10

1                             5                                      ?

2                             ?                                       ?

a. Find values for investment and output for for periods 2 through 5.

b. Now let's imagine that the farmer starts by investing 100 instead of 1.  Find investment and output for the next five periods just as in part a.

t                               I                                      Y

0                             100                               100

1                             50                                   ?

2                             ?                                       ?

c.  Now, on one graph, with time (t) on the horizontal axis, plot output over the first six periods when the farmer starts by investing 1 and then plot output when he starts by investing 100.  See if you can notice what's happening here.

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