Final answer:
Government purchases in the Solow Growth model influence capital accumulation, which can impact output per worker and long-term economic growth. The effect depends on whether the spending is financed through taxation or borrowing, and whether it is directed towards productive investments.
Step-by-step explanation:
Government purchases, when introduced into the Solow Growth model with a constant population, can potentially impact the economic growth measured as output per worker, which is modeled by y_l = A * k, where y_l is output per worker, A represents technology, and k is capital per worker. When the government spends, it can either finance its purchases through taxation or by borrowing. Higher taxes can reduce the disposable income of consumers, leading to lower consumption and savings, which in turn can reduce investment in the Solow model and thus impact capital accumulation.
In contrast, if the government borrows to finance its spending, this can lead to an increase in the interest rate and 'crowd out' private investment, also potentially leading to lower capital accumulation. This impact on capital affects the output per worker since, in the Solow model, growth is driven by capital deepening (increased k) and technological advancements (increases in A). Nevertheless, if government spending is directed towards productive investments, such as infrastructure, education, or research and development, it could enhance productivity and technological progress, contributing positively to long-term growth.