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It the real rate of interest on borrowing is $5$ percent per annum and housing prices rise at $2$ percent, then according to the neoclassical theory of investment with the price of houses at $100$, the rental for houses (over the year) must be?

The price of property after an year will be $102$ and the person will receive an interest of $5$. Therefore, the rent should be $(102+5)-100=7$? Is this correct?

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No, it's not correct. It's generally assumed that in the absence of risk (which I believe you should ignore in this question), investment in different types of assets should yield the same returns. If I had \$100k I could lend it at 5% earning \$5k of interest after a year. Alternatively I can buy \$100k house now and sell it in a year. If I do that I get the difference in price (\$2k) and rental income. What the rental income must be so that those two types of investment are equally good.

(For easier exposition I assumed that interest rate on borrowings and savings are the same. The logic, however, is exactly the same).

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  • $\begingroup$ Thanks so much! So the rent will be $3$? $\endgroup$ Apr 28, 2017 at 10:59
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    $\begingroup$ Yes but make sure you understand that it will be 3% of the house's value, not just $3K or whatever. Year 1 the rent would be 100 * .03 = 3. year 2 the house's value would be 102 meaning that the rent would be 102 * .03 = 3.06. $\endgroup$ Apr 28, 2017 at 13:34

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