He4002 Quiz 2 March 9 2019 Instructions Do The Following 4 Questions As A Take Home 3164828

HE4002 Quiz 2 March 9, 2019 Instructions: Do the following 4 questions as a take-home quiz. Please do not discuss with others. Please show efforts on how you derive the results. Please write your name and matric number on each page of your answers. Please also staple your answer sheets. 1. Introduce government spending in the basic Solow model. The growth accounting equation now becomes: Y (t) = C(t) + I(t) + G(t). Production function still takes the standard Cobb-Douglas form: Y (t) = AK(t) aL(t) 1-a where A is a constant and total population grows at rate n. Assume government spending is given by G(t) = sY (t). (a) Derive the physical capital accumulation equation. Show how the quantity of physical capital per worker, k * , is determined. Is it possible to have multiple steady-state equilibrium? (b) Suppose now that government spending partly comes out of private consumption, so that C(t) = (1 – s – ?s)Y (t), where ? ? [0, 1]. Discuss how the value of s affects the equilibrium outcome of the model? (c) Now suppose that a fraction f of G(t) is invested in the capital stock, so that total investment at t is given by: I(t) = (s – (1 – ?)s + fs)Y (t) show that if f is sufficiently high, the steady-state level of capital-labor ratio will increase as a result of higher s. 2. Assume representative agent’s utility function takes form: max Z 8 0 (1 – s(t))h(t)dt 1 where 0