Question

Suppose a consumer has a utility function U(X,Y) = MIN (X,Y) + X + Y. Using a graph, illustrate the indifference curve that goes through the bundle X = 3, Y = 3.

I have the answer but could someone explain to me how to approach the solution and what each part means.

Answer 1

If you make 100 bundles of X and Y as follows (1 to 10 units of Y for 1 unit of X, 1 to 10 units of Y for 2 units of X, and so on) and calculate the utility for each bundle you get the following table. It is easy to do in excel by using a formula like this for utility function and copying it across the 100 bundles: =MIN($A3,B$2)+$A3+B$2

MIN(X,Y) + X + Y	Y
X	1	2	3	4	5	6	7	8	9	10
1	3	4	5	6	7	8	9	10	11	12
2	4	6	7	8	9	10	11	12	13	14
3	5	7	9	10	11	12	13	14	15	16
4	6	8	10	12	13	14	15	16	17	18
5	7	9	11	13	15	16	17	18	19	20
6	8	10	12	14	16	18	19	20	21	22
7	9	11	13	15	17	19	21	22	23	24
8	10	12	14	16	18	20	22	24	25	26
9	11	13	15	17	19	21	23	25	27	28
10	12	14	16	18	20	22	24	26	28	30

You can see easily that 4 units of utility can be obtained either by having

(1 unit of X and 2 of Y)

or

(2 units of X and 1 of Y)

So 1, 2 and 2, 1 on the graph show points of indifference. Similar other points can be plotted to get different indifference curves (with higher and lower values of utility)

Now, back to the question, which indifference curve goes thru the bundle 3, 3 (X=3, Y=3)

In the table above this bundle represents a utility = 9

The other bundles which have the same quantity of utility are:

1,7

2,5

5,2

7,1

If we plot these (and 3,3) we get the indifference curve for utility = 9 as follows: