Consider the Ramsey model with the household having logarithmic preferences and production function satisfying our usual assumptions writtenin intensive form as y = f(k). Consumption (per unit of effective labour) is denoted by c, capital (per unit of effective labour) is denoted by k and output (Per unit of effective labour) is denoted by y. The equation for the c = 0 locus is given by L'(k)= p + g. where p > 0 is the rate of time preference, g> 0 is the rate of technological progress and where f'(k) denotes the first derivative of the function f. The equation for the k = 0 locus is given by c = f(k) (n + g)k The growth rate of population is denoted by n with the depreciation rate of capital being assumed to be zero. As usual the symbol dot over a variable denotes the time derivative, eg, k denotes the time derivative of k. (a) Display the c = 0 and the k = 0 locus in a phase diagram with the endogenous variables c and k along the two axes explaining your reasons behind the qualitative shapes of the two loci. Discuss how the economy reaches the steady state in this phase diagram. (b) Assume that there is an unexpected rise in the rate of time preference p for households. Explain how this change affects the two loci (if at all) in a new phase diagram and how the economy moves to the new steady state. (c) Compare and contrast the effects of a permanent and a temporary increase in government purchases when these purchases are financed by lump sum taxes and the government runs a balanced budget at every point of time.
Consider the Ramsey model with the household having logarithmic preferences and production function satisfying our usual assumptions writtenin intensive form as y = f(k). Consumption (per unit of effective labour) is denoted by c, capital (per unit of effective labour) is denoted by k and output (Per unit of effective labour) is denoted by y. The equation for the c = 0 locus is given by L'(k)= p + g. where p > 0 is the rate of time preference, g> 0 is the rate of technological progress and where f'(k) denotes the first derivative of the function f. The equation for the k = 0 locus is given by c = f(k) (n + g)k The growth rate of population is denoted by n with the depreciation rate of capital being assumed to be zero. As usual the symbol dot over a variable denotes the time derivative, eg, k denotes the time derivative of k. (a) Display the c = 0 and the k = 0 locus in a phase diagram with the endogenous variables c and k along the two axes explaining your reasons behind the qualitative shapes of the two loci. Discuss how the economy reaches the steady state in this phase diagram. (b) Assume that there is an unexpected rise in the rate of time preference p for households. Explain how this change affects the two loci (if at all) in a new phase diagram and how the economy moves to the new steady state. (c) Compare and contrast the effects of a permanent and a temporary increase in government purchases when these purchases are financed by lump sum taxes and the government runs a balanced budget at every point of time.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Hello, please help me to solve the question about the Ramsey model, as attached.
Transcribed Image Text:Consider the Ramsey model with the household having logarithmic preferences
and production function satisfying our usual assumptions writtenin intensive form
as y = f(k). Consumption (per unit of effective labour) is
denoted by c, capital (per unit of effective labour) is denoted by k and output
(Per unit of effective labour) is denoted by y. The equation for the c = 0 locus
is given by
L'(k) = p + g.
where p > 0 is the rate of time preference, g> 0 is the rate of technological progress
and where f'(k) denotes the first derivative of the function f. The equation for the k =
0 locus is given by
c = f(k) - (n + g)k
The growth rate of population is denoted by n with the depreciation rate of capital
being assumed to be zero. As usual the symbol dot over a variable denotes the time
derivative, eg, k denotes the time derivative of k.
(a) Display the c = 0 and the k = 0 locus in a phase diagram with the
endogenous variables c and k along the two axes explaining your reasons
behind the qualitative shapes of the two loci. Discuss how the economy
reaches the steady state in this phase diagram.
(b) Assume that there is an unexpected rise in the rate of time preference p for
households. Explain how this change affects the two loci (if at all) in a new
phase diagram and how the economy moves to the new steady state.
(c) Compare and contrast the effects of a permanent and a temporary increase in
government purchases when these purchases are financed by lump sum
taxes and the government runs a balanced budget at every point of time.
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