Utility function is given as Cobb Douglas functional form: U =Price the first good: P₁ = 5$Price the second good: P₂ = 10$Income: I = 500$0.5 0.5 A)a) Find the Budget equation and derive the slope of this budget equation.b)Set up the Utility Maximization Problem (UMP) or Primal Problem and Construct theLagrangian functionc)Find the Marshallian (Uncompansated) demand functions and calculate the optimalquantities of goods: X₁ and X₂d)Compute Indirect Utility Function (Value Function) and maximum Utility value.e)Find the equation of the Indifference Curve (IC) and calculate the slope of this Indifferencecurve (Marginal rate of substitution: MRS) at the optimal point (tangency point)f)Verify that at consumer equilibrium point "slope" of Indifference Curve (MRS) is equal to"slope" of Budget Constraint Equation (Relative Price Ratio)B)C)a)Set up the Expenditure Minimization Problem (EMP) or Dual Problem and construct theLagrangian functionb)Find the Hicksian (Compansated) demand functions and and calculate the optimal quantitiesof goods: X₁ and X₂Calculate Expenditure functionc)d)Show that both Marshallian and Hicksian demands functions initially provide identicalnumerical valuesa)If the price of the first good decrease to 4$ (p₁ = 4$) then find the new (final) Marshallianand Hicksian demand functions for the first and second goodsb)Find the difference between new and old Marshallian demands for the first good:(x₁ new x₁ old). This difference is called as the "Total Effect" (TE)c)Find the difference between new Hicksian demand and old Marshallian demands for the firstgood. This difference is called as the "Substitution Efect" (SE).d) Find the difference between new Marshallian demand and and new Hicksian demand. Thisdifference is called as the "Income Effect" (IE)e) Show that TE = SE + IE

Utility function : x10.5 x20.5 Price of good 1 : p1 = 5 Price of good 2 : p2 =10 Income = 500 Above…

Answered: 0.5, Utility function is given as Cobb…

0.5, Utility function is given as Cobb Douglas functional form: U = x1.5x2.5 Price the first good: P₁ = 5$ Price the second good: P₂ Income: I = 500$ = 10$

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

Utility function is given as Cobb Douglas functional form: U =
Price the first good: P₁ = 5$
Price the second good: P₂ = 10$
Income: I = 500$
0.5 0.5

A)
a) Find the Budget equation and derive the slope of this budget equation.
b)
Set up the Utility Maximization Problem (UMP) or Primal Problem and Construct the
Lagrangian function
c)
Find the Marshallian (Uncompansated) demand functions and calculate the optimal
quantities of goods: X₁ and X₂
d)
Compute Indirect Utility Function (Value Function) and maximum Utility value.
e)
Find the equation of the Indifference Curve (IC) and calculate the slope of this Indifference
curve (Marginal rate of substitution: MRS) at the optimal point (tangency point)
f)
Verify that at consumer equilibrium point "slope" of Indifference Curve (MRS) is equal to
"slope" of Budget Constraint Equation (Relative Price Ratio)
B)
C)
a)
Set up the Expenditure Minimization Problem (EMP) or Dual Problem and construct the
Lagrangian function
b)
Find the Hicksian (Compansated) demand functions and and calculate the optimal quantities
of goods: X₁ and X₂
Calculate Expenditure function
c)
d)
Show that both Marshallian and Hicksian demands functions initially provide identical
numerical values
a)
If the price of the first good decrease to 4$ (p₁ = 4$) then find the new (final) Marshallian
and Hicksian demand functions for the first and second goods
b)
Find the difference between new and old Marshallian demands for the first good:
(x₁ new x₁ old). This difference is called as the "Total Effect" (TE)
c)
Find the difference between new Hicksian demand and old Marshallian demands for the first
good. This difference is called as the "Substitution Efect" (SE).
d) Find the difference between new Marshallian demand and and new Hicksian demand. This
difference is called as the "Income Effect" (IE)
e) Show that TE = SE + IE

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B)
a)
Set up the Expenditure Minimization Problem (EMP) or Dual Problem and construct the
Lagrangian function
b)
Find the Hicksian (Compansated) demand functions and and calculate the optimal quantities
of goods: X₁ and X₂
c) Calculate Expenditure function
d)
Show that both Marshallian and Hicksian demands functions initially provide identical
numerical values

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