4. Columns 1 through 4 in the table at the top of the page show the marginal uti

Question

4. Columns 1 through 4 in the table at the top of the page show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respec- tively, $18, S6, S4, and $24 and that Ricardo has an income of $106. LO7.2 a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.

Explanation / Answer

Ans:-
a) We have to use the general formula for finding the optimum utility maximizing quantities. First find that we need to compute the marginal utilities per dollar of every product by dividing marginal utility with price.
Units of A MUA MUA/PA MUB MUB/PB MUC MUC/PC MUD MUD/PD
1 72 4.00 24 4.00 15 3.75 36 1.50
2 54 3.00 15 2.50 12 3.00 30 1.25
3 45 2.50 12 2.00 8 2.00 24 1.00
4 36 2.00 9 1.50 7 1.75 18 0.75
5 27 1.50 7 1.17 5 1.25 13 0.54
6 18 1.00 5 0.83 4 1.00 7 0.29
7 15 0.83 2 0.33 3.5 0.88 4 0.17
8 12 0.67 1 0.17 3 0.75 2 0.08
Consumer optimum is achieved for two goods if the marginal utility derived from the last dollar spent on one good equals the marginal utility received from the last dollar spent on the other. Here we see that MUA/PA = MUB/PB = MUC/PC = 2.00 when Ricardo consumes 4 units of A, 3 units of B and 3 units of C. This makes a total of 18*4 + 3*6 + 3*4 = 102. He will not purchase product D.
b) His savings are $3
c) As mentioned. we have MUA/PA = MUB/PB = MUC/PC = 2.00

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