Ramsey models

1. Do immigrants hurt native workers? Covid-19 has forced border closure throughout the world. This has virtually stopped global migration. Some pundits in Australia argue that stopping the flow of migrants to Australia should be a key part of the recovery from the Covid19 shock. They argue that migrants hurt local workers. In this question, we will use the Ramsey model below to analyze the issue C'(t) ak(t)\"_l p 6'9 C(T) a W) = Mt)\" cit) Go) (n + 90W) where G represents government spending, production is Cobb-Douglas Y0?) = Kit)'(A(t)I/(t))1'', the growth rate of technology is g = A/A(t), and the growth rate of the population is n = L/L(t). Finally, assume that growth rate of population is broken into two components such that n=not+im where not stands for the portion of the growth rate explained by the existing population and am is the growth rate due to immigration. Note that if immigration is set to zero that n = not. (a) Using a phase digram, show what happens when the growth from immigration falls (im J.) permanently. Include the relevant saddle paths and arrows to show the dynam- ics. (3 points) (b) Solve for the balance growth path values of capital per effective worker Us\") and con- sumption per effective worker (c*) in terms of a, 9, p, n, G, and g. (2 points) (c) On the balanced growth path, does the growth rate of consumption per worker depend on im? (2 points) (d) Using your response to questions (a), (b), and (c), does it appear that immigration hurts natives in the short run? What about in the long run? (4 points) (e) Describe one assumption of this model that if it is not true, it would fundamentally change your conclusion. Provide an explanation why. You may also use another model we have learned in this class to justify your concern. (Note: marks will be awarded for the quality of your argument.) (4 points)