Given the following demand function for artichokes, which of the options below is correct? Q=200- 40P + 5I- 11Pb+ 14Pc Q=quantity demanded of artichokes P= price of artichokes in dollars I=...

Given the following demand function for artichokes, which of the options below is correct?

Q=200- 40P + 5I- 11Pb+ 14Pc

Q=quantity demanded of artichokes

P= price of artichokes in dollars

I= average household income in thousands of dollars per year

Pc= price of carrots

Pb= price of butter

According to the demand function from above:

(a) artichokes are inferior

(b) the law of demand is violated

(c) artichokes are a Giffen good

(d) carrots and artichokes are substitutes

(e) there is an excess demand for artichokes

What's the answer and how did you find it/ why is it correct

pohnpei397 | Certified Educator

The correct answer to this question is Option D.  Artichokes and carrots are, according to the demand function shown here, substitutes.  When the price of carrots rises, the quantity demanded for artichokes rises as well.  This shows that the two are substitutes.

We can eliminate all of the other options by using the function.  We see that the price has a negative value (-40P).  This means that when price increases (all other things being equal), quantity drops.  This means that the law of demand is not violated (so B is not correct) and artichokes are not a Giffen good so C is not the correct answer.  We can see that the income has a positive value (5I).  This means that when income rises (all other things being equal) the quantity demanded of artichokes will also rise.  Therefore, this is not an inferior good, so A is not the correct answer.  Finally, E is not correct because we have no idea what supply is for artichokes so we cannot know if demand is excessive.

We can also tell that D is correct and artichokes and carrots are substitutes.  The price of carrots has a positive value (14Pc).  This means that (all other things being equal) an increase in the price of carrots will lead to an increase in the quantity demanded of artichokes.  If we hold P, I, and Pb constant any increase in Pc leads to an increase in Q.  This shows that artichokes and carrots are substitutes and D is the correct answer.
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