Lecture 8 - Extensions of the Solow Growth Model

Question 1

If s = 0, what would the level of consumption be?

Answer 1

• if s = 0, all income is consumed in the first period
• nothing is saved
• no income to consume thereafter
• i.e. c = 0

Question 2

If s = 1, what would the level of consumption be?

Answer 2

• if s =1, all income is saved
• nothing is left to consume
• i.e. c = 0

Question 3

Why is it ambiguous what an increase in s will do to level of consumption in the steady state (c*)?

Answer 3

• an increase in s:
• leads to higher k* and y* , which may raise c*
• reduces consumption’s share of income (1-s), which may lower c*

Question 4

Define k*gold, the Golden Rule level of capital

Answer 4

the steady state value of k that maximises consumption

Question 5

Express c* in terms of k*

Answer 5

• c* = y* - i*
• c* = f(k*) - i꙳
• c* = f(k*) - (δ+n)k꙳
• in general i = Δk + (δ+n)k
• in steady state i* = (δ+n)k* because Δk = 0

Question 6

Show that c* is largest where the slope of the production function equals the slope of the break-even investment line

Answer 6

• c* = f(k*) - (δ+n)k꙳
• maximise it wrt to k*
• f’(k*) - (δ+n) = 0
• f’(k*) = MPK = δ+n

Question 7

Does the economy have a tendency to move toward the Golden Rule steady state?

Answer 7

no

Question 8

What do policy makers need to do in order to achieve the Golden Rule?

Answer 8

adjust savings rate s