1. Given the utility function U = 1/2 1/3 (a) Determine the value of the marginal utilities (b) Hence estimate the change in U if ₁ and 22 both increase by 1 unit. (c) Does the law of diminishing marginal utility hold for this function? (Take a look at pg 376 Jacques) and when 2₁ = 25 and 2₂ = 8.

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Th Course: 20222 X
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IGC Is GDP an adequate... 3 Methods of GDP...
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Lecture 1: Rev X
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1. Given the utility function U = x₁x₂
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Mathematics for Economics II: ECON1004
Tutorial 2: Implicit Differentiation & Optimization
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(a) Determine the value of the marginal utilities and when #₁ = 25 and 2 = 8.
(b) Hence estimate the change in U if ₁ and 2 both increase by 1 unit.
(c) Does the law of diminishing marginal utility hold for this function?
(Take a look at pg 376 Jacques)
where C = f(Y) = 95.05 +0.712Y
■
O Search
2. Find the partial elasticities of z w.r.tz for the function z = x²y³
3. Find the derivative of y w.r.tz for the function 2x² + 6xy + y² = 18 using implicit differen-
tiation.
4. Differentiate the following function w.r.t z using the Implicit Function Theorem:
eyr²y = 1
■
(Theorem given on Slide 17 & 18 of Lecture 2 part II)
5. The following is a standard macroeconomic model for an economy open to international trade:
Y=C+I+X-M
b Success Confi x +
Highlight
V
Erase
I
re
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Transcribed Image Text:PDF Th Course: 20222 X ← C IGC Is GDP an adequate... 3 Methods of GDP... === Lecture 1: Rev X 1 of 2 Q 77°F Partly cloudy Set Microsoft Edge as the default application for reading PDF files? Lecture 1: Rev X https://myelearning.cavehill.uwi.edu/pluginfile.php/1848585/mod_resource/content/2/ECON1004 Lesson summary: th... + ECON1004 Tu X C Find the deriv X ▸ (42) What is a X Corporate Social Re... Relationships betw... Set as default Tutorial_2.pdf 1/2 1/3 1. Given the utility function U = x₁x₂ | Page view| A Read aloud | (T) Add textDraw V Mathematics for Economics II: ECON1004 Tutorial 2: Implicit Differentiation & Optimization Qbartleby - Sea X Social Responsibilit... Functionalist Theory (a) Determine the value of the marginal utilities and when #₁ = 25 and 2 = 8. (b) Hence estimate the change in U if ₁ and 2 both increase by 1 unit. (c) Does the law of diminishing marginal utility hold for this function? (Take a look at pg 376 Jacques) where C = f(Y) = 95.05 +0.712Y ■ O Search 2. Find the partial elasticities of z w.r.tz for the function z = x²y³ 3. Find the derivative of y w.r.tz for the function 2x² + 6xy + y² = 18 using implicit differen- tiation. 4. Differentiate the following function w.r.t z using the Implicit Function Theorem: eyr²y = 1 ■ (Theorem given on Slide 17 & 18 of Lecture 2 part II) 5. The following is a standard macroeconomic model for an economy open to international trade: Y=C+I+X-M b Success Confi x + Highlight V Erase I re Other favorites Z ... 10:00 pm 15/02/2023 X
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