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# 7) Consider the Solow growth model and the following production function: Y= K^0.3(AL)^0.7 A) If A= 2, L= 20,000 and K=400 what is Output ? B)

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7) Consider the Solow growth model and the following production function: Y= K^0.3(AL)^0.7 A) If A= 2, L= 20,000 and K=400 what is Output ? B) Suppose the Labor force grows by 5% so that it is now 21,000. By how much does output increase? C) Starting again with the conditions in part a, what is capital increases by 5%so that it is now 420. By how much does output increase? 8) In the neoclassical growth model we express the investment function as i= sf(k), where i is investment per worker, s is the saving ratio, k is capital per worker, and y is output per worker. A) plot the saving function, i= sf(K) and output function y=f(k)=k1/2, where s=0.3and values of k vary between 4 and 9 B) Find consumption per worker for k=4 and k=9 10) Consider Kremers 0-ring model. There are 4 workers in this economy , Jack , Fred, Melbaand Daphne. Suppose that there are two firms and each firm hires only two workers ,each workers , each of whom has skill level equal to q (q is assumed to lie between 0 and 1, with 1 being the highest skill level. Two of the workers (Jack and Melba) are highly skilled ( q=0.9) ; the other two ( Fred and Daphne) are less skilled ( q=0.3). Output is given by the product of the q-levels for example firm 1 might hire a high skill worker and a low skill worker. Output of thsi firm would be 0.9*0.3= 0.27 Individual Income in 1990 Income in 2000 1 100 100 2 100 100 3 100 100 4 100 100 5 100 800 6 500 800 Total income 1000 2000
A) Calculate the total output that would be produced by these two firms under each of the following scenarios: Firm A hires Jack and Fred and Firm B hires Melba and Daphne. Firm A hires Jack and Melba and Firm B hires Fred and Daphne Under which scenario is output highest? B) Repeat the above calculations but with highly skilled workers having a q value of 0.6 and low skill workers 0.5. How do your results differ form those in part a? C) What do these results suggest about sorting of workers in an economy? 11) Consider the following income distributions: A) Plot the Lorenz Curves for 1990 and for 2000. Be sure to label your graph clearly. B) Calculate the Gini coefficient for 1990 and for 2000 ( the area between the Lorenz curve and the outside of the box is 0.33 for 1990 and 0.27 for 2000). C) What do you conclude about changes in income inequality form 1990 to 2000 Individual Income in 1990 Income in 2000 1 100 100 2 100 100 3 100 100 4 100 100 5 100 800 6 500 800 Total income 1000 2000

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7) Consider the Solow growth model and the following production function: Y=
K^0.3(AL)^0.7
A) If A= 2, L= 20,000 and K=400 what is Output ?
Solution:
Y = K^0.3(AL)^0.7
= (400)^0.3 (2*20,000)^0.7
=...

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