Graph your results of part a through part c. In what sense does this problem involve only a single commodity—peanut butter and jelly sandwiches? Graph the demand curve for this single commodity. Discuss the results of this problem in terms of the income and substitution effects involved in the demand for jelly.
Ebrima gets $3 per month 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 $.05 per ounce) and jelly (at $.10 per ounce). Bread is provided free of charge by a concerned neighbor. Ebrima is a picky 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.
- How much peanut butter and jelly will Ebrima buy with his $3 allowance in a week?
- Suppose the price of jelly were to rise to $.15 per ounce. How much of each commodity would be bought?
- By how much should Ebrima’s allowance be increased to compensate for the rise in the price of jelly in part b?
- Graph your results of part a through part c.
- In what sense does this problem involve only a single commodity—peanut butter and jelly sandwiches? Graph the demand curve for this single commodity.
- Discuss the results of this problem in terms of the income and substitution effects involved in the demand for jelly.
Expert Answer
Two goods or services are said to be complements for each other when the utility to be derived from a good becomes enhanced if it is consumed in companion with the other and/or if one good doesn't yield any utility at all in the absence of the other. Complementary goods are consumed in pairs and have a negative cross-price elasticity of demand.
For example, vehicles & fuel, bread & butter, rim & tire, pencil & eraser, etc.
Since 1 ounce of Jelly is mixed with 2 ounces of peanut butter by Person E to prepare a sandwich, peanut butter and jelly will be treated as complementary goods.
The budget function of the consumer will be given as follows:
I = Px.X + Py.YI = Px.X + Py.Y
where,
II is the income/allowance received by the consumer.
XX is units of Good X.
YY is units of Good Y.
PP stands for the price of a good.
The budget line, in this case, would be:
3 = 0.1J+ 0.05P3 = 0.1J+ 0.05P
Since 2 ounces of peanut butter is fixed with 1 ounce of jelly, the consumer will consume different quantities of both goods in a ratio of 2:1. The indifference curves will be L shaped with the vertex representing a combination in the aforementioned ratio as any other point on the indifference curve will not yield any
Utility Function:
U = Min(2X, Y)U = Min(2X, Y)
where,
XX is units of Good X.
YY is units of Good Y.
In this case, the utility function can be represented as U = Min(2J, P)U = Min(2J, P).
The utility-maximizing principle requires that the consumer consumes both goods in fixed proportions i.e.
2J = P2J = P
Substituting this in the budget line:
3 = 0.1J+ 0.05P3 = 0.1J+ 0.05(2J)3 = 0.20JJ = 15∴ P = 303 = 0.1J+ 0.05P3 = 0.1J+ 0.05(2J)3 = 0.20JJ = 15∴ P = 30
Ans. 1. Person E will buy 15 ounces of Jelly and 30 ounces of peanut butter to maximize his utility.
If the price of Jelly increases to $0.15, the budget line of Person E will change to the following.
3 = 0.15J+ 0.05P3 = 0.15J+ 0.05P
Substituting the value of P in terms of J in the new budget line:
3 = 0.15J+ 0.05P3 = 0.15J+ 0.05(2J)3 = 0.25JJ = 12∴ P = 243 = 0.15J+ 0.05P3 = 0.15J+ 0.05(2J)3 = 0.25JJ = 12∴ P = 24
Ans. 2. Person E will buy 12 ounces of Jelly and 24 ounces of peanut butter to maximize his utility at new prices.
To compensate for the rise in the price of Jelly, the income must be increased in a manner that the consumer can afford the previous bundle of consumption. To find the change in income, we must substitute the old consumption bundle in the new budget line:
I2 = 0.15J+ 0.05PI2 = 0.15(15)+ 0.05(30)I2 = 2.25+ 1.50I2 = $3.75I2 = 0.15J+ 0.05PI2 = 0.15(15)+ 0.05(30)I2 = 2.25+ 1.50I2 = $3.75
Change in income required to compensate for the price change:
∆I = I2 − I1∆I = 3.75 − 3.00∆I = $0.75∆I = I2 - I1∆I = 3.75 - 3.00∆I = $0.75
Ans. 3. Person E's allowance must be increased by $0.75 to compensate for the rise in the price of jelly.
Please help me part 4,5,6 respectively and tanks for your support i really appreciate it
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