David N. gets $3 per week as an allowance to spend any way he pleases. Because he likes only peanut butter and jelly sandwiches, he spends the entire amount on peanut butter (at $0.05 per ounce) and jelly (at $0.10 per ounce). Bread is provided free of charge by a concerned neighbor. David is a particular eater and makes his sandwiches with exactly 1 ounce of jelly and 2 ounces of peanut butter. He is set in his ways and will never change these proportions.

(a) How much peanut butter and jelly will David buy with his $3 allowance in a week?
(b) Suppose the price of jelly were to rise to $0.15 an ounce. How much of each commodity would be bought?

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saqib097 saqib097 · Answer 1 · 2020-03-06T09:29:46+01:00

Answer:

The solution to the given problem is done below.

Explanation:

(a) How much peanut butter and jelly will David buy with his $3 allowance in a week?

According to the given problem, David likes 2 ounces of peanut butter for every 1 ounce of jelly,

2Pb = J and the budget constraint is .05pb+.1j = 3.

By using substitution.

David will buy Pb = 30 ounces, J = 15 ounces.

30(0.05) + 15 (0.10) = 3

(b) Suppose the price of jelly were to rise to $0.15 an ounce. How much of each commodity would be bought?

If pj = $0.15,

24(0.05) + 12(0.15) = 3

Substitution now yields J = 12 ounces, Pb = 24 ounces.