Question

Suppose that apples cost $1. A consumer feels that they are willing to give up 4 apples in order to consume a banana, as long as they are consuming 10 or less bananas. After the 10th banana their appreciation for them is not as high, so they are willing to trade 2 apples for an additional banana, as long as their banana consumption is less than or equal to 20. After the 20th banana they are fed up of bananas and would not give up a single apple for a banana. Note: All parts are worth 10 points. Questions: (1) What is the demand curve for bananas (a picture, fully lablled, is enough) (2) Assume the supply curve for bananas is S(p)=5p. What is the equilibrium price and quantity in the market for bananas? (3) Suppose that there is a natural disaster in apple growing countries, so now the price of apples is $2. Assume that the resources used in banana production are not suitable for apple production, so this change in the price of apples leaves supply of bananas unaffected. What is the new equilibrium price and quantity in the market for bananas?

Answer 1

1) Since the price of banana is not given, let us take willingness to pay as the price in terms of price of apples. So if an apple costs $1, and consumer si willing to give up 4 apples for each banana, hence, he is willing to pay $4 for each banana upto 10 bananas. His willing to pay drops to $2 per banana as he is ready to give only 2 apples per banana after 10th banana. His willingness to pay drops to zero after 20th banana. So shape of demand curve would look like stairs( shown in fig1).

2) Supply function: S(p) =5p

Then supply function will cut demand curve at quantity of 10 bananas. Hence equilibrium quantity will be 10 bananas. The equibrium price will be between $2.

3). Now since the price of apples has increased to $2, and nothing has been said about whether price will affect his willingness to give up apples for bananas in the given quantity. So let us assume consumer is still willing to give up 4 apples for bananas upto 10th bananas. So price he is willing to pay now will be $8 ($2 *4 apples) per bananas upto 10. After 10th banana, he is willing to pay $4 ($2* 2apples) for each banana upto 20th banana. And after 20th banana, he is willing to pay zero for bananas. So, considering the same supply curve for banana, we can see from the figure ,given below as (Fig.2), that suoply curve cuts the demand curve at quantity of 20 banana and price of $4. So new equilibrium quantity will be 20 banana and equilibrium price will be $4.