1 Solow growth model (25 points)Consider a Solow growth model with exogenous technological growth but no population growth.Let N denote the number of fixed labor supply in each period. Suppose that output is producedaccording to the constant return to scale production function,

where Zt, and Kt, denote respectively the labor-augmenting productivity, and capital in periodt. In addition, Zt evolves according to

The law of motion for capital stock is

. The aggregate consumption Ct equals a constant fraction, I - s, of aggregateproduction,

, and the aggregate investment equals the remaining fraction s ofaggregate production,

【題組】

1 (5 points) Define st as output per effective worker, i.e.,

and k as capital per effiectiveworker, i.e,

. Uise the constant return to scale production function to express therelationship between y and k.