Consider Romer's model of ideas with production given by y(t) = K (t)a (A(t) Ly(t)) -a,...

  

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Consider Romer's model of ideas with production given by y(t) = K (t)a (A(t) Ly(t)) ¹-a, 0 < a < 1, where Y(t) is aggregate real output, K(t) is aggregate capital, A(t) is aggregate technology, and Ly (t) is the number of people working in the goods sector. Capital accumulates according to: K(t) = SY(t)- 8K (t), where 0 < s < 1, and 0 < 6 < 1. In the "ideas" sector, new technology is produced according to: A(t) = 0A(t) PLA (t)^, where 8 > 0, 0 < < 1, and 0 < < 1. The model is closed by assuming that the number of workers in the ideas sector, LA (t), is given by: LA(t) = SAL(t), where 0 < SA < 1 (all other workers work in the goods sector), and total population L(t) grows at rate n > 0. 1.1. Provide an economic interpretation for the parameter 0. (5%) Y(t) = 1.2. If we define output-per-effective-person as: y(t): A(t) L(t)' then derive an expression for steady state output-per-effective-person that depends only on parameters and explain the effect that an increase in 0 has on this steady state. Be sure to show all your working. Explain what your steady state expression implies about absolute convergence. 1050US Consider Romer's model of ideas with production given by y(t) = K (t)a (A(t) Ly(t)) ¹-a, 0 < a < 1, where Y(t) is aggregate real output, K(t) is aggregate capital, A(t) is aggregate technology, and Ly (t) is the number of people working in the goods sector. Capital accumulates according to: K(t) = SY(t)- 8K (t), where 0 < s < 1, and 0 < 6 < 1. In the "ideas" sector, new technology is produced according to: A(t) = 0A(t) PLA (t)^, where 8 > 0, 0 < < 1, and 0 < < 1. The model is closed by assuming that the number of workers in the ideas sector, LA (t), is given by: LA(t) = SAL(t), where 0 < SA < 1 (all other workers work in the goods sector), and total population L(t) grows at rate n > 0. 1.1. Provide an economic interpretation for the parameter 0. (5%) Y(t) = 1.2. If we define output-per-effective-person as: y(t): A(t) L(t)' then derive an expression for steady state output-per-effective-person that depends only on parameters and explain the effect that an increase in 0 has on this steady state. Be sure to show all your working. Explain what your steady state expression implies about absolute convergence. 1050US

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Interpretation of Parameter The parameter represents the rate of technological progress in the ideas sector It measures the impact of new ideas on the ... View the full answer