Consider a modified Solow Growth Model:

F(K, EN) = K\"(bN)1'a, where b is the labour augmenting technology, which grows at a rate f, i.e., bt+1 = (1 + f)bt. For simplicity, assume that the total factor productivity z = 1, and the population is constant, i.e., N; = N for all t. The rest of the model is the same as in the stande Solow model in the textbook. Especially, the aggregate capital stock evolves according to Kt+1 = I; + (1 d)Kt. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter a: be the variable per effective unit of worker; that is a: = %. 1. List all the equilibrium conditions of this model. 2. Using the equilibrium conditions you listed above, write down an expression that describes the evolution of the aggregate capital stock, Kg over time. Briey explain why this ex- pression is not particularly convenient for our analysis of the model? 3. Then, using your answer to the above question, show that the capital stock per eectve unit of worker, kt, evolves over time according to the following equation. (1+flkt+1 =8k?+(1d)kt- (1) Why is this expression more useful for our analysis than what you get in the above ques- tion? (Even if you cannot do this part of the exam, use this expression (1) for the remainder of the exam. Keep moving on!) 4. Show in a diagram that there exists a unique long-run equilibrium with constant k > 0. 5. Find the expressions for such let, say 39*, in terms of the model parameters. 6. What is the growth rate of consumption per capita at the steady state? 7. Suppose the economy is at the steady state. Now, suppose there is a permanent increase in the rate of technological progress (f). Explain what it means to this economy. Especially, \" and how it evolves overtime before discuss how the economy responds to this \"shoc , and after the shock. Is it better to have a higher growth rate of technology? And why? Discuss