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In which situation does the demand and supply curve both shift? My professor told me for the demand curve, the income of the consumers changes etc. will shifted the demand curve; For the supply curve, the changes technology etc will shift the supply curve.

So is this statement true: Only the types of situation with some factors causes the demand curve shift along with some other separate factors causes the supply curve shift may had both curve shift simultaneously, but in fact there is no single one factor that could shift both curve simultaneously.

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No, this case is not true.

A factor which both shifts supply and demand curves at the same time is an increase or decrease in population.

This both adds consumers (increase in demand) to the economy and increases the workforce (increase in labor force, thus producing more and increasing quantity supplied).

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A change in labor wage could bring about a simultaneous change in the market demand and supply curves.

Assume that wages increase: consumers now have more income and this in principle will affect the demand curve. On the other hand, the costs of the firms have increased, and this will affect the supply curve.

The same could be said in case space rents increase: it results in an increase in (asset) income for consumers/asset holders, and an increase in costs for firms renting the space.

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