Suppose that the consumer has $8 to spend on A and B. The price of A is $1, while the price of B is $2?

Question

Can someone explain me how the answer is 4 here?

Total Utility of A and B

Quantity of A Total Utility of A Total Utility of B

1 5 16

2 9 28

3 12 36

4 14 40

5 15 40

12. In the table above, suppose that the consumer has $8 to spend on A and B. The price of A is $1, while the price of B is $2. At the utility-maximizing bundle, what is the marginal utility per dollar of the last units purchased of A and B?

A) 16

B) 8

C) 6

D) 4

E) 1

Can you please explain me how the answer is 4 here. ( As per Answer key)

I am really confused.

Answer 1

D) 4

Q . TU(a) . TU(b) MU(a) MU(b)

1 ...... 5 ..... 16 ..... 5 ..... 16

2 ...... 9 ..... 28 ..... 4 ..... 12

3 ..... 12 ..... 36 ..... 3 ...... 8

4 ..... 14 ..... 40 ..... 2 ...... 4

5 ..... 15 ..... 40 ..... 1 ...... 0

Consumer equilibrium condition states:

MU(a) / P(a) = MU(b) / P(b)

So with given prices equilibrium will be:

MU(a) / 1 = MU(b) / 2

MU(a) = MU(b) / 2

Budget is 8 so budget equation is 8=1*a + 2*b or:

a=8-2b

Now only left to find quantity of goods which satisfies both conditions:

a=8-2b

MU(a) = MU(b) / 2

So b≠0 (a≠8) , b≠1 (a≠6) ,  b≠4 (a≠0) ,  it means that b could only be 2 or 3

[1] MU(b=2)=12 ; a=4 ; MU(a=4)=2

[2] MU(b=3)=8 ; a=2 ; MU(a=2)=4

Combination [2] fits condition MU(a) = MU(b) / 2 or

4=8/2

Conclusion: MU(a)/P(a) = 4 (at a=2), thus option "D" is right.

Answer 2

TAX