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We now introduce the government sector into a solow model. Let us assume that the production function is: Y = K L1 - where 0 << 1. Now Y = C + I + G and we know that G = BY with 0 < < 1. We further assume that C = c(Y - G) where ca is a constant between zero and one. The population growth rate is n. The depreciation rate is \delta. Let y = Y/L, k = K/L and c = C/L. a) Is the production function constant returns to scale (CRTS) ? Prove it. b) As is standard, k = sy - (n + \ delta )k holds. Find out the steady state values of k, y and c in this model (i.e. the values of k*, y* and c *). c) What will happen to the steady state you find in part a) if increases ? d) Find out the values of k, y, and c in the golden rule steady state (i.e. the values of k**, y** and c**). e) What saving rate can be used to support this golden rule steady state ?

We now introduce the government sector into a solow model. Let us assume that the production function is: Y = K L1 - where 0 << 1. Now Y = C + I + G and we know that G = BY with 0 < < 1. We further assume that C = c(Y - G) where ca is a constant between zero and one. The population growth rate is n. The depreciation rate is \delta. Let y = Y/L, k = K/L and c = C/L. a) Is the production function constant returns to scale (CRTS) ? Prove it. b) As is standard, k = sy - (n + \ delta )k holds. Find out the steady state values of k, y and c in this model (i.e. the values of k*, y* and c *). c) What will happen to the steady state you find in part a) if increases ? d) Find out the values of k, y, and c in the golden rule steady state (i.e. the values of k**, y** and c**). e) What saving rate can be used to support this golden rule steady state ?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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We now introduce the government sector into a Solow model. Let us assume that the production function is: Y = K L1 - where 0 << 1. Now Y = C + I + G and we know that G = BY with = 0 << < 1. We further assume that C = c@(Y - G) where c is a constant between zero and one. The population growth rate is n. The depreciation rate is \delta. Let y = Y/L, k = K/L and c C/L. a) Is the production function constant returns to scale (CRTS) ? Prove it. b) As is standard, k = sy - (n + \ delta )k holds. Find out the steady state values of k, y and c in this model (i.e. the values of k*, y* and c *). c) What will happen to the steady state you find in part a) if increases ? d) Find out the values of k, y, and c in the golden rule steady state (i.e. the values of k**, y** and c**). e) What saving rate can be used to support this golden rule steady state ?
Transcribed Image Text:We now introduce the government sector into a Solow model. Let us assume that the production function is: Y = K L1 - where 0 << 1. Now Y = C + I + G and we know that G = BY with = 0 << < 1. We further assume that C = c@(Y - G) where c is a constant between zero and one. The population growth rate is n. The depreciation rate is \delta. Let y = Y/L, k = K/L and c C/L. a) Is the production function constant returns to scale (CRTS) ? Prove it. b) As is standard, k = sy - (n + \ delta )k holds. Find out the steady state values of k, y and c in this model (i.e. the values of k*, y* and c *). c) What will happen to the steady state you find in part a) if increases ? d) Find out the values of k, y, and c in the golden rule steady state (i.e. the values of k**, y** and c**). e) What saving rate can be used to support this golden rule steady state ?
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