Multisector Ramsey Model

Question 1

Kuznets-Madison facts

Answer 1

Question 2

Set up of the multisector Ramsey model

Answer 2

Question 3

Household preferences

Firms production function

Answer 3

• CES
• Each sector has a CD with labor augmenting technological progress.
  
  • alpha is the same for every sector

Question 4

Household problem

Answer 4

• They choose consumption composition
• Savings

Question 5

Elasticity of subsitution between goods

Answer 5

Question 6

Euler equation and expenditure shares

Answer 6

• Expenditures shares in this model are constant
• r is interest rate deflated by aggregate price index

Question 7

Assumptions on the production side

Answer 7

• Capital good are produced from manufactures in a 1-1 basis
• Labor an capital are perfecly mobile across industries

Question 8

Firm problem

Answer 8

• Relative factor use is same across all sectors
• Relative product prices are given by relative productivities (slide 16)
  
  • There are more units in the market => their price have to be lower

Question 9

Equilibrium definition

Answer 9

Walras law implies clearing for manufacturing market

• Manufacture production=manufacture consumption + gross investment

Question 10

Nominal output share definition

Answer 10

• The first term is the definition. The last one is an implication of the model
• Capital share of the sector is also equal to the labor share

Question 11

Structural change

Answer 11

• We have structural change only when saving rate is changing
• There is no structural change within consumption goods sectors

Question 12

Law of motion of capital

Answer 12

Question 13

Dynamic system

Answer 13

=> allocations between sectors are irrelevant for aggregate variables

Question 14

General conclusions of the model

Answer 14

• Aggregate capital, consumption and output behave as in the one sector Ramsey model
• Along the BGP there is no structural change
• In the transition to the SS, there is no structural change between the agricultural and services sectors