Marginal Utility Assignment: Consumption Basket and Effects

This assignment solution delves into the concept of marginal utility, analyzing a consumer's optimal consumption basket for coffee and milk. It begins by demonstrating why a specific consumption bundle is not optimal. The solution derives the marginal rate of substitution and determines the optimal consumption basket. The assignment then explores how changes in the price of coffee affect the optimal consumption, calculating the new optimal basket and determining whether coffee is a Giffen good for the consumer. Furthermore, the solution breaks down the income and substitution effects associated with a price increase. Finally, it describes the relationship between the consumer's demand for coffee and their income, referencing the previous findings and using correct economic terminology. The solution includes relevant references to support the analysis.

MARGINAL UTILITY 1
Marginal Utility
Course
Name
Institution Affiliation
Question 1: Without deriving the optimal consumption basket, show that the basket with x
= 25 cups of coffee, and y = 50 litres of milk, is NOT optimal. (3 marks)
Optimal Bundle= M U x
M U y
= Px
Py

MARGINAL UTILITY 2
4
1 ≠ 50
25
4
1 ≠ 2
1
It is therefore not an optimal bundle since it doesn’t meet the condition for optimality.
Question 2: Derive the expression for Sally's marginal rate of substitution. (1 Mark)
Marginal Rate of substitution is given by dy
dx = M U x
M U y
=
20
√ x
1
= 20
√ x
Question 3: Find Sally's optimal consumption basket. (3 Marks)
Optimal Bundle= M U x
M U y
= Px
Py
20/ √ 25
1 = 4
1

MARGINAL UTILITY 3
20/5
1 = 4
1
= 4
Sally should consume 4 times as much for milk for every cup of coffee
200 = Px X + PyY
200 = 4x + y
but y = 4x
200 = 4x + 4x
= 200 = 8x
x = 25
y = 100
Question 4: Find Sally's new optimal consumption basket if the price of coffee increases
to Px = $5 per cup. (3 Marks)
M U x
M U y
= Px
Py
M U x
M U y
= 5
1

MARGINAL UTILITY 4
Sally should consume 5 times as much for milk for every cup of coffee
200 = Px X + PyY
200 = 4x + y
but y = 4x
200 = 4x + 5x
= 200 = 9x
x = 22.22
y = 111.11
Question 5: Is co_ee a Gi_en good for Sally? Briey explain. Your answer must reference the
consumption baskets you found in questions 3 and 4. (3 Marks)
No, Coffee is not a giffen good to Sally. This is because when the price of coffee increases from
$4 to $5, she reduces the consumption of coffee while increasing the consumption of milk. If
coffee was a giffen good, she should have increased the quantity demanded for coffee (Kauder,
2015).

MARGINAL UTILITY 5
Question 6: Find the income and substitution effects associated with an increase in the
price of coffee from $4 to $5 a cup. (4 Marks)
In this case, when the price of coffee increases, the budget line shifts from B1 to B2.
Sally changes her optimal bundle of goods from A to B. The movement from A to B is the total
effect of the price change. With regard to the substitution effect, coffee is more expensive than
milk and therefore Sally changes her consumption. With regard to the income effect, the real
U2
U1
x2 x3 x1
total
inc
sub
C
B A
B3
B2
B1

MARGINAL UTILITY 6
income decreases since the bundle B is at a lower indifference curve than A. The total effect is
therefore the income effect plus the substitution effect (Finkelstein and Notowidigdo, 2013). In
order to demonstrate this, we draw a budget line B3 which is parallel to B2 and is tangent to U1.
At point C, the price increase is taken into consideration. The movement from A to C is the
substitution effect while the movement from B to C is the income effect as the consumption
decreases when the budget line moves from B3 to B2 (Cook and and Nakagawa, 2013).
Question 7: Describe the relationship between Sally's demand for co_ee and her income.
Your answers must reference the your previous answers, AND use the correct term to
describe the relationship (3 Marks)
It is clear that Sally’s demand for coffee has a positive relationship with income. Increase in real
income may lead to Sally consuming more coffee while decrease in real income may lead to
Sally drinking less coffee. From the optimal basket it is evident that an increase in the price of
coffee which decreases real income leads to a reduction in the quantity of coffee in the basket
(Clark and Fawaz, 2015).
References
Clark, A.E. and Fawaz, Y., 2015. Retirement and the marginal utility of income.
Cook, K.S., Cheshire, C., Rice, E.R. and Nakagawa, S., 2013. Social exchange theory.
In Handbook of social psychology (pp. 61-88). Springer Netherlands.

MARGINAL UTILITY 7
Finkelstein, A., Luttmer, E.F. and Notowidigdo, M.J., 2013. What good is wealth without health?
The effect of health on the marginal utility of consumption. Journal of the European
Economic Association, 11(suppl_1), pp.221-258.
Kauder, E., 2015. History of marginal utility theory. Princeton University Press.