Economics Assignment: Utility Maximization and Production Analysis

This economics assignment delves into two core microeconomic concepts: consumer utility maximization and production functions. The first question explores a young wine connoisseur's optimal purchasing decisions between French Bordeaux and McLaren Vale Shiraz under varying price conditions, analyzing how changes in the price of one good affect the consumer's utility. The second question focuses on a farm's production function, determining cost-minimizing levels of labor and capital. Finally, the assignment provides the comparison between autarky and free trade equilibrium for the United States and for France, with the help of diagram. Desklib provides a platform for students to access this assignment and many other solved papers.

Running head: ECONOMICS
Economics
Name of the student
Name of the university
Author note

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ECONOMICS
Table of Contents
Answer 1....................................................................................................................................3
Answer a)...................................................................................................................................5
Answer b)...................................................................................................................................5
Answer c)...................................................................................................................................6
Answer 2....................................................................................................................................7
Answer a.....................................................................................................................................7
Answer b....................................................................................................................................8
Answer c.....................................................................................................................................8
Answer d....................................................................................................................................8
Answer e.....................................................................................................................................8
Answer f.....................................................................................................................................8
Answer 3....................................................................................................................................9
Reference list............................................................................................................................11

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Answer 1
U ( wB , wS ) =wB
2/ 3 wS
1 /3
given his budget constraint
pB wB + pS wS ≤ I
M wB= du
d wB
=2
3 wB
2
3 −1
wS
1 /3
M wS= du
d wS❑
= 1
3 wB
2
3 wS
1
3 −1
M wB
M wS
= 2wS
1 /3
3 wB
1/ 3 ÷ 1 wB
2
3
3 wS
2 /3
M wB
M wS
= 2 wS
wB
Given,

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Price of wB= £20 and price of wS is £8
As,
M wB
M wS
= P wB
P wS
M wB
M wS
= 2 wS
wB
=20
8
wS = 5
4 wB
Here income is given as I,
Therefore inserting this equation in
pB wB + pS wS ≤ I
We get
20wB + 8 ( 5
4 wB) = I (since, wS =¿ 5/4wB)
20wB + 10 wB =I
wB =I/30

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wS = 5
4 × I
30
wS = I
24
Answer a)
Given total income as I, consumer will purchase I/30 French Bordeaux wine and I/24 Vale
Shiraz wine.
Answer b)
when price of wB is £ 10, then
M wB
M wS
= 2 wS
wB
=10
8
Given,
pB wB + pS wS ≤ I
10wB + 8 ( 5
8 wB) = I
15wB = I

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wS =5
8 wB
wB =I /15
Therefore,
wS =5
8 × I/15
=I/24
Amount of French Bordeaux will be I /15 and amount of McLaren Vale Shiraz purchased
will be I/24.
Answer c)
The young wine connoisseur will be better off in part b since he can buy more units of
French Bordeaux when the price drops to £10,
since I
30 < I
15

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Answer 2
Q = 60L1/2 K1/4 …….. EQUATION 1
Q = 60L1/2 K1/4
Answer a
Constaint is
Wl+ rk
For minimization let
F= wL +rk +ƛ[60L1/2 K1/4 -Q]
df/ dL= w + ƛ 1/2 ×60L1/2-1 K1/4
df/ dk= r + ƛ 1/4×60K-3 L1/2/4
-ƛ = W L1/2 /30 K1/4
-ƛ = Rk3/4 / 15 L1/2
W L1/2 /30 K1/4 = rk3/4 / 15 L1/2
Now, 2rK = wL , cost minimising output of L and K are.
K* =Wl/2r
L*= 2rk/w
Putting in the equation 1 we get
Q= 60(2rk/w)1/2 (wL/2r)1/4

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Answer b
Putting the values,
120= 60 (20k/6)1/2 (6L/20)1/4
Answer c
Long run TC = w L + r K
Q = 60 (2rK/W)1/2 (WL/2r)1/4
TC = w(2rK/W) + r(WL/2r)
TC = 2rk + Wl/2
Answer d
120= 60L1/2 K1/4
Answer e
L = 2rK/W
K= WL/2r
Answer f
K=Lw/2r
=6L/20
L=2rK/w
=20K/6

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x
Answer 3
Figure 1 comparison of autarky and free trade equilibrium
The above diagram compares the situation between autarky and free trade equilibrium
for the United States and for France. The PPF of US is given by the red line and the green
PPF represents France. It is assumed that both the countries have the same preference and
same size labour force. Also, US have absolute advantage in the production of cheese and
France have the absolute advantage in the production of wine. Therefore, it can be also said
that each country have the competitive advantage in that particular good which they are
selling. In case of free trade, the consumption points of US is C and production is P. As the
indifference curve (free trade) IFT lies in the northeast of IAut which is the autarky
indifference curve, the national welfare of the US will be increasing as US moves to free
trade. On the other hand the production and consumption point of France is given by green

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P* and C*. the indifference curve of France is IFT* and the autarky is IAut*. Here also as
national welfare rise, france will move to free trade.

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Reference list
Bade, Robin, and Michael Parkin. Foundations of microeconomics. Pearson, 2015.
Baumol, William J., and Alan S. Blinder. Microeconomics: Principles and policy. Nelson
Education, 2015.
Bowles, Samuel. "Marx and modern microeconomics." (2018).
Cowen, Tyler, and Alex Tabarrok. Modern principles of microeconomics. Macmillan
International Higher Education, 2015.
Fine, Ben. "Microeconomics." University of Chicago Press Economics Books (2016).
Friedman, Lee S. The microeconomics of public policy analysis. Princeton University Press,
2017.
Kreps, David M. Microeconomics for managers. Princeton University Press, 2019.
McKenzie, Richard B., and Dwight R. Lee. Microeconomics for MBAs: The economic way of
thinking for managers. Cambridge University Press, 2016.