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Carrots and potatoes are grown using the same factors of production. Figure X shows the demand (D$_c$) and supply (S$_c$) curves for carrots. Figure Y shows the demand (D$_p$) and supply (S$_p$) curves for potatoes. A change in people’s preferences shifts the demand for carrots from (D$_{c1}$) to (D$_{c2}$). As a result, the supply of potatoes shifts from (S$_{p1}$) to (S$_{p2}$).

Which one of the following statements correctly explains the changes shown in Figures X and Y?

1 ) 

The demand curve for carrots shifts due to the rationing function of prices

2 ) 

The price of carrots increases because carrots and potatoes are in derived demand

3 ) 

The price of potatoes increases because potatoes and carrots are in joint supply

4 ) 

The supply curve for potatoes shifts due to the incentive function of prices

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