At Olive’s Oranges customers may pick oranges from a 100-tree orchard at the price of 15¢ per orange. Olive’s orchard currently produces 8,000 oranges annually. Olive estimates that installing a new irrigation system would increase her annual yield by 200 oranges, beginning next year. The irrigation system requires an immediate cost of $600.
(i) Calculate the marginal product of capital for the irrigation system. Express your answer as a percentage of the cost of the capital.
(ii) Suppose the interest rate is 4%. Should Olive invest in the irrigation system? Why or why not?
(iii) Repeat part ii for an interest rate of 8%.
(i) If Olive invests in the irrigation system, then the value of her future harvests rises by $30 per year (200 oranges ? 15¢ per apple). The increased yield represents 5% of the $600 cost, so the marginal product of capital is 5%.
(ii) If the interest rate is 4%, then Olive should purchase the irrigation system. Since MPK > r, investing in capital provides a better return than lending funds. The annual interest on a loan of $600 is only $24, which is smaller than the $30 benefit obtained from the capital investment.
(iii) If the interest rate is 8%, then Olive should not purchase the irrigation system. Since MPK < r, lending funds provides a better return than does the new irrigation system. The annual interest received from a $600 loan is $48, while the annual benefit from the irrigation system is only $30.
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