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According to the economist’s definition, investment is the purchase of capital goods (factories, machinery, tools and so on) with the intention to earn higher return and attain future wealth.
Construction of a new headquarters and family buys a newly constructed home from a developer can be considered as an investment, both indicating the increase in capital stock. Thus, both option 1 and 4 can be considered as an investments.
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Buying share, buys an older home, purchases stores are not an investment, because, buying share is related to financial asset and buys an older home is already produced and not a new one, thus, it does not leads to increase the capital stock. In the case of purchasing store, it is already bankrupt, thus, does not increase the capital stock. Therefore, option 2, 3 and 5 are not considered as an investment.