Question

Jane spends all of her $200 weekly income on two goods, X and Y. Her utility function is given by U(X,Y) = 2XY, If the price of X = $4/ unit and the price of Y = $10 a unit, how much of Y should she buy?

Answer 1

From the above question, we have the following information

Weekly Income = $200

Price of X = $4/unit

Price of Y = $10/unit

So from this information, we can make our budget equation which will be

4X + 10Y = 200 (where X and Y are number of units)

Now we will find the possible values of X and Y which will satisfy this budget equation

X	Y
50	0
45	2
40	4
35	6
30	8
25	10
20	12
15	14
10	16
5	18
0	20

So these combinations or bundles will satisfy the budget equation.

Now we have utility function as U(X, Y) = 2XY so we will put each and every bundle and see which bundle gives the highest utility.

X	Y	U = 2XY
50	0	0
45	2	180
40	4	320
35	6	420
30	8	480
25	10	500
20	12	480
15	14	420
10	16	320
5	18	180
0	20	0

As (25, 10) gives the highest utility hence Jane will spend her weekly income of $200 by buying 25 units of X at $4 per unit and 10 units of Y at $10 per unit.

So according to the question, Jane should buy 10 units of Y