Consider an economy that lasts for two periods. A household receives nominal labour income Y₁ = 100 in the first period and Y₂ = 110 in the second period. The price level in the first period is P₁ = 10 and in the second period it's P₂ = 11. The nominal interest rate i is 15%. Household chooses real consumption c₁ and c₂ (relative to price level in the first period) to maximise utility U(C₁, C₂) that exhibits the decreasing marginal rate of substitution property. 1. 2. 3. Calculate the inflation rate and the real interest rate r. Find the real consumption values for which the household neither saves, nor borrows. For all questions below assume that this is the optimal choice for the housheold. Draw and describe analytically the set of feasible consumption choices. What is the marginal rate of substitution at the optimal choice? 4. a) Now assume that due to increase in risk premia, banks introduce a spread on interest rates, borrowers now pay r = r +1% and lenders get r₁ = r - 1% on their savings. Show graphically how this affects the set of feasible consumption choices. b) Can the introduction of the interest rate spread affect the optimal consumption choice of the household? Why/Why not?

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Hello, i have completed the other questions im just showing for context, i need assistance on 4a and 4b highlighted on the picture.

would love to get some assistance from an expert.

Thank you in advance!

Consider an economy that lasts for two periods. A household receives nominal labour income Y1 = 100
= 110 in the second period. The price level in the first period is P = 10
in the first period and Y2
and in the second period it's P2 = 11. The nominal interest rate i is 15%. Household chooses real
consumption c1 and c2 (relative to price level in the first period) to maximise utility U(cı, c2) that
exhibits the decreasing marginal rate of substitution property.
1.
Calculate the inflation rate T and the real interest rate r.
2.
Find the real consumption values for which the household neither saves, nor borrows.
For all questions below assume that this is the optimal choice for the housheold.
3.
Draw and describe analytically the set of feasible consumption choices. What is the
marginal rate of substitution at the optimal choice?
4.
Now assume that due to increase in risk premia, banks introduce a spread on interest
rates, borrowers now pay r, = r + 1% and lenders get ri = r – 1% on their savings. Show
graphically how this affects the set of feasible consumption choices.
b)
Can the introduction of the interest rate spread affect the optimal consumption choice
of the household? Why/Why not?
Transcribed Image Text:Consider an economy that lasts for two periods. A household receives nominal labour income Y1 = 100 = 110 in the second period. The price level in the first period is P = 10 in the first period and Y2 and in the second period it's P2 = 11. The nominal interest rate i is 15%. Household chooses real consumption c1 and c2 (relative to price level in the first period) to maximise utility U(cı, c2) that exhibits the decreasing marginal rate of substitution property. 1. Calculate the inflation rate T and the real interest rate r. 2. Find the real consumption values for which the household neither saves, nor borrows. For all questions below assume that this is the optimal choice for the housheold. 3. Draw and describe analytically the set of feasible consumption choices. What is the marginal rate of substitution at the optimal choice? 4. Now assume that due to increase in risk premia, banks introduce a spread on interest rates, borrowers now pay r, = r + 1% and lenders get ri = r – 1% on their savings. Show graphically how this affects the set of feasible consumption choices. b) Can the introduction of the interest rate spread affect the optimal consumption choice of the household? Why/Why not?
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