Please answer part B only.Please note the second image is a hint! xi represents the consumption of eachgood iA planned economy is an economic systemin which a government or ruler makes mostor all of the important decisions about theproduction and distribution of goods andservices in the society. Therefore,o In a planned economy the totalconsumption should be at least as muchas the total production.. i.e. pix1 + P2X2 <= P¡Y1 + P2Y2 a) A planner in a small, open economy has a utility functionU = x1x2and production takes place according to the production functionsY1 = 10L, – 0.5L?Y210L2 – L3The world prices of the goods are p110 and P25. The total amount of labouravailable in the economy is 5 units.(i)Formulate the Lagrange equation.(ii)Write down the Karush-Khun-Tucker conditions.(iii)Determine a possible solution.b) Let aggregate national income be given byY; = C; + It + G;Where C, I and G are consumption, investment and government expenditure. Assumethat consumption is given byC = mY;%3DInvestment is given byI; = i + «(Y¢-1– Y;-2)%3DAnd government expenditure declines over time according toG¢ = Go(1 – 8)*,0 < 8 < 1Where 8 is the exogenous rate of decline of government expenditure(i)Derive the linear second order difference equation.(ii)Solve the difference equation.

Macroeconomics examines large-scale economic factors and aggregate changes in areas such as…

b) Let aggregate national income be given by Yt = Ct + It + Gt Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Investment is given by Ct = mYt It = 1 + a(Yt-1 - Yt-2) And government expenditure declines over time according to Gt = Go (1 - 8)t, 0 < 8 <1 Where & is the exogenous rate of decline of government expenditure Derive the linear second order difference equation. Solve the difference equation. (i) (ii)

b) Let aggregate national income be given by Yt = Ct + It + Gt Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Investment is given by Ct = mYt It = 1 + a(Yt-1 - Yt-2) And government expenditure declines over time according to Gt = Go (1 - 8)t, 0 < 8 <1 Where & is the exogenous rate of decline of government expenditure Derive the linear second order difference equation. Solve the difference equation. (i) (ii)

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Please answer part B only. Please note the second image is a hint!

xi represents the consumption of each
good i
A planned economy is an economic system
in which a government or ruler makes most
or all of the important decisions about the
production and distribution of goods and
services in the society. Therefore,
o In a planned economy the total
consumption should be at least as much
as the total production.
. i.e. pix1 + P2X2 <= P¡Y1 + P2Y2

a) A planner in a small, open economy has a utility function
U = x1x2
and production takes place according to the production functions
Y1 = 10L, – 0.5L?
Y2
10L2 – L3
The world prices of the goods are p1
10 and P2
5. The total amount of labour
available in the economy is 5 units.
(i)
Formulate the Lagrange equation.
(ii)
Write down the Karush-Khun-Tucker conditions.
(iii)
Determine a possible solution.
b) Let aggregate national income be given by
Y; = C; + It + G;
Where C, I and G are consumption, investment and government expenditure. Assume
that consumption is given by
C = mY;
%3D
Investment is given by
I; = i + «(Y¢-1– Y;-2)
%3D
And government expenditure declines over time according to
G¢ = Go(1 – 8)*,
0 < 8 < 1
Where 8 is the exogenous rate of decline of government expenditure
(i)
Derive the linear second order difference equation.
(ii)
Solve the difference equation.

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