If good x is a normal good and y is its gross substitute then:

Question

(a) Income elasticity of the demand for x must be greater than zero and so must be cross price elasticity; (b) Income elasticity of the demand for x is less than zero and so is the cross price elasticity; (c) Income elasticity of the demand for x must be greater than zero and cross price elasticity must be less than zero; (d) Income elasticity of the demand for x must be less than zero and cross price elasticity greater than zero.

Answer 1

I'll help you understand the material and find the answer on your own:

Keep in mind what a normal good is: The more money you have, the more you buy.

For example, housing is very much a normal good: Lower-income people rent rooms in other people's houses or at the YMCA, or share apartments. Somewhat better off folks rent their own apartments. People who are better off still rent two- or three-bedroom apartments to raise their families in. Well to do folks own houses.

(And then...there are McMansions. Finally, bungalows in California. ;) )

Income elasticity is the percentage change in the demanded divided by the percentage change in income. For example, if Mary gets a 20% raise at work, and cuts her spending on beans and rice by half (aka 50%), then her income elasticity for beans and rice is -50%/20% = -2.5.

Two goods are gross substitutes if, when the price of one goes up, people buy more of the other. 

The cross price elasticity of demand between two goods is the percentage change in demand for one good divided by the percentage change in price of the other.

For example, suppose John only buys peanut butter and jelly to make PBJs (peanut butter and jelly sandwiches) -- he doesn't like plain peanut butter sandwiches or plain jelly sandwiches. Suppose the price of peanut butter goes up by 10%, and in response he buys 15% less jelly. John's cross price elasticity for peanut butter and jelly is -15%/10% = -1.5.

Good luck!

Answer 2

The answer is the first option, that is, income elasticity of  the demand for x must be greater than zero and so must be cross price elasticity. 

 

Now the explanation:

 

Let me take the first part of the answer (Income elasticity) - 

 

 

Income elasiticity (e_I) is the responsiveness of demand to the changes in income.

 

e_I  =  Percentage change in quantity demanded / Percentage change in income.

 

Hence, a positive income elasticity means that with the increase in income, the quantity demanded for a good increases; and with the decrease in income, the quantity demanded for the same good decreases. In such a case, the good is considered to be a normal good.

 

For example -  An income of a person increases by 20%.  Following the pay hike, his white bread consumption also increases by 10% . This gives us income elasticity of white bread = 0.5 (10% / 20% ). This implies that white bread is a normal good as the income elasticity is greater than zero.

 

Therefore, if x is a normal good then it means that the income elasticity for x is positive.

 

 

Now to the second part of the answer (Cross price elasticity) - 

 

 

Cross price elasiticity (e_xy) is the responsiveness of demand for a good x to the changes in the price of good y.

e_xy = Percentage change in quantity demanded for good x / Percentage change in price of good y.

 

Hence, a positive cross price elasticity shows that if the price of good y increases then the quantity demanded for good x  increases. This means that with the increase in price of good y, people buy less of good y and shift to good x and so increase the demand for good x. This shift of demand implies that the  goods are substitutes of each other. 

 

Therefore, a positive cross price elasticity means that the two goods are gross substitutes.

 

For example - If the price of brown bread increases by 10%, then people demand less of it and shift to other bread (lets say to white bread), thereby increasing its demand by (lets assume) 20% . This gives us cross price elasticity of white and brown breads 2 (20% / 10%).  Cross price elasticity of 2 (greater than zero) tells us that the two goods are gross substitutes of each other.

 

Finally, white bread (good x) is a normal good as income elasticity is positive and brown bread (good y) is a gross substitute for white bread as their cross price elasticity is positive.

 

I hope, i am able to satisfy your query.