Question

Consider a utility function u(x1,x2)u(x_1, x_2) where:

MU1=2x11x42MU_1 = 2x_1^{1} x_2^{4}

MU2=4x21x32MU_2 = 4x_1^{2} x_2^{3}

The consumer with this utility function is consuming an optimal bundle (x∗1,x∗2)=(4,6)(x_1^*, x_2^*) = (4, 6) when the price of good 1 is p1=2p_1 = 2. What is the consumer’s income?

Answer 1

We know at optimal condition the Marginal Utility to Price ratio is equal for all goods.

So,

So, Using the data given in question we can write the Optimal condition as :-

So,

So, Using Optimal Bundle value given

Now, We know Consumers Income (I) is given as :-

As we know the Prices and using the Optimal bundle we can write :-

Hence, Consumer's Income is $24