Question

*3. The demand for organic carrots is given by the following equation where Po is the price of organic carrots, Pc is the price of conventional carrots, and / is the average consumer income Notice how this isn't a standard demand curve that just relates the quantity of organic carrots demanded to the price of organic carrots. This demand function also describes how other factors affect demand-namely, the price of another good (conventional carrots) and income. a. Graph the inverse demand curve for organic carrots when P5 and 1- 10. What is the choke price? b. Using the demand curve drawn in (a), what is the quantity demanded of organic carrots when P0-5? When Po 10? c. Suppose Pc increases to 15, while I remains at 10. Calculate the quantity demanded of organic carrots. Show the effects of this change on your graph and indicate the choke price. Has there been a change in the demand for d. What happens to the demand for organic carrots when the price of conventional carrots increases? Are organic and e. What happens to the demand for organic carrots when the average consumer's income increases? Are carrots a organic carrots, or a change in the quantity demanded of organic carrots? conventional carrots complements or substitutes? How do you know? normal or an inferior good?

Answer 1

Q = 75 - 5Po + Pc + 2I

(a) Pc = 5, I = 10

Q = 75 - 5Po + 5 + 20

Q = 100 - 5Po

Graph of demand curve as follows

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The choke price can be found by solving for the price that corresponds to a quantity demanded of zero:P O=20–(0.2 ×0) =20

(b)

When Po = 5, Q = 100 - (5 x 5) = 100 - 25 = 75

When Po = 10, Q = 100 - (5 x 10) = 100 - 50 = 50

(c)

Po = 10, Pc = 15, I = 10

From original demand curve,

Q = 75 - 5Po + Pc + 2I

= 75 - (5 x 10) + 15 + (2 x 10)

= 75 - 50 + 15 + 20

= 60

Since own price is unchanged, this increase (caused by price of substitute) is a rightward shift in demand. The new demand curve is D1. There has been change in demand of organic carrot (not quantity demanded of organic carrot).

d) When price of conventional carrot increases, demand for organic carrot increases (coefficient of Pc is positive). This means, they are substitutes.

e)

When income increases, demand for organic carrot increases (coefficient of I is positive). This means carrots are normal goods.