Answer the question on the basis of the following two schedules,which show the amounts of additional satisfaction (marginal utility)that a consumer would get from successive quantities of products J and K. $\begin{array}{c}
\begin{array}{ccc}
Unit&&\
\text { of } J & & M U_{j} \
\hline
1 & & 56 \
2 & & 48 \
3 & & 32 \
4 & & 24 \
5 & & 20 \
6 & & 16 \
7 & & 12
\end{array}
\begin{array}{ccc}
Unit&&\
\text { of } K & & M U_{k} \
\hline
1 & & 32 \
2 & & 28\
3 & & 24\
4 & & 20\
5 & & 12\
6 & & 10\
7 & & 8
\end{array}
\end{array}$ Refer to the data.If the consumer has money income of $52 and the prices of J and K are $8 and $4 respectively,the consumer will maximize her utility by purchasing:
A) 2 units of J and 7 units of K.
B) 5 units of J and 5 units of K.
C) 4 units of J and 5 units of K.
D) 6 units of J and 3 units of K.

Question

Quizplus · Accepted Answer

To maximize utility, the consumer must allocate her entire budget such that the marginal utility per dollar spent is equal for both goods. 
MUj/Pj = MUk/Pk 
From the given data: 
MUj/Pj when J = 1: 56/8 = 7 
MUj/Pj when J = 2: 48/8 = 6 
MUk/Pk when K = 1: 32/4 = 8 
MUk/Pk when K = 2: 28/4 = 7 
MUk/Pk when K = 3: 24/4 = 6 
Therefore, the optimal combination of J and K is where the consumer spends all her budget and the marginal utility per dollar spent is equal for both goods. 
Using the given budget of $52: 
2J + 7K = 52 
Re-arranging and solving for J: 
J = (52 - 7K) / 2 
Substituting different values of K in the above equation gives: 
When K = 1, J = 22.5 (not possible as we cannot buy a fraction of a unit) 
When K = 2, J = 22 
When K = 3, J = 17.5 (not possible as we cannot buy a fraction of a unit) 
When K = 4, J = 13 
When K = 5, J = 8.5 (not possible as we cannot buy a fraction of a unit) 
When K = 6, J = 4 
When K = 7, J = - 0.5 (not possible as we cannot buy a negative quantity) 
The only feasible combination is therefore 4 units of J and 5 units of K.

Answer the Question on the Basis of the Following Two