Question

If she spends all of her income on bananas and melons, Natalie can just afford 9 bananas and 10 melons per day. She could also use her entire budget to buy 3 bananas and 12 melons per day. The price of banana is 8 yen each. (a) How much is Natalie’s income per day? Show the budget set of Natalie on a graph. (b) If the price of banana increases to 16 yen each what should be Natalie’s income that makes 9 bananas and 10 melon still affordable. Show your result on a graph.

Answer 1

a)

Let the price of Melon be X

Natalie can just afford 9 bananas and 10 melons per day i.e. Income, I is given by

I=9*8+10*X=72+10X -----(1)

Natalie can also buy 3 bananas and 12 melons per day. So, income I is given by

I=3*8+12*X=24+12X -----(2)

We know that Income in both cases is equal. So,

72+10X=24+12X

48=2X or X=24

So, Price of Melon=24 Yen

So, we can found income either by equation (1) or equation (2). I consider equation (1)

I=72+10X=72+10*24=312 Yen

If B denotes the number of banana consumed per day and M denotes the number of melons consumed per day, then budget constraint is given by

8B+24M=312

Following consumption set is feasible with the given income and prices.

B	M=(312-8B)/24
0	13
3	12
6	11
9	10
12	9
15	8
18	7
21	6
24	5
27	4
30	3
33	2
36	1
39	0

b)

Suppose the revised price of banana is 16 Yen and price of Melon is same i.e 24 Yen.

Income required to meet the consumption level of 9 banana and 10 Melons is given by

I=16*9+24*10=384 Yen

Revised budget constraint becomes

16B+24M=384

Following schedule can be generated with the help of given information.

B	M=(384-16B)/24
0	16
3	14
6	12
9	10
12	8
15	6
18	4
21	2
24	0

Revised budget constraint is depicted in the graph attached with part (a)

Desired consumption level is common to both constraints. This possible consumption level is enclosed by a rectangle.