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. $KMUk13222832442051261078\begin{array}{c}\begin{array}{ccc}Unit&&\\\text { of } J & & M U_{j} \\\hline1 & & 56 \\2 & & 48 \\3 & & 32 \\4 & & 24 \\5 & & 20 \\6 & & 16 \\7 & & 12\end{array}\begin{array}{ccc}Unit&&\\\text { of } K & & M U_{k} \\\hline1 & & 32 \\2 & & 28\\3 & & 24\\4 & & 20\\5 & & 12\\6 & & 10\\7 & & 8\end{array}\end{array}$ 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

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.

KMUk13222832442051261078\begin{array}{c}\begin{array}{ccc}Unit&&\\\text { of } J & & M U_{j} \\\hline1 & & 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} \\\hline1 & & 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.

Juliana Gomez · Accepted Answer

Final Answer : C, Explanation :  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/PkFrom the given data:MUj/Pj when J = 1: 56/8 = 7MUj/Pj when J = 2: 48/8 = 6MUk/Pk when K = 1: 32/4 = 8MUk/Pk when K = 2: 28/4 = 7MUk/Pk when K = 3: 24/4 = 6Therefore, 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 = 52Re-arranging and solving for J:J = (52 - 7K) / 2Substituting 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 = 22When K = 3, J = 17.5 (not possible as we cannot buy a fraction of a unit)When K = 4, J = 13When K = 5, J = 8.5 (not possible as we cannot buy a fraction of a unit)When K = 6, J = 4When 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.

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