Question

15. Consider an economy, with a production function given by Y-AK03L07. This economy's annual GDP growth rate is 5%. Also assume that L and Kare both growing at annual rates of 2%. Calculate the growth rate of total factor productivity for this economy. a. 2.0% b. 3.0% 4.0% c. d. 5.0% 16. Suppose output is determined by a Cobb-Douglas production function Y=AK L1 Where 0ca<1. If total factor productivity (A) remains constant, but labour (L) and capital (K) inputs both double, output will: a. Double b. Increase by A Increase by 2 times A c. d. Increase by (1/2) times A 17. In the Solow-Swan model, if saving is less than replacement investment then, other things being equal a. The capital-labour ratio will fall and the marginal product of capital will fall b. The capital-labour ratio will rise and the marginal product of capital will fall The capital-labour ratio will fall and the marginal product of capital will rise c. d. The capital-labour ratio will rise and the marginal product of capital will rise 18. Consider a situation in which the capital labour ratios of all countries lie below the steady state level in the Solow Swan model. Which of the following is most correct? a. Per capita income in countries with different capital-labour ratios and the same total factor productivity growth rate will grow at the same rate b. Per capita income in countries with the same capital-labour ratios and different total factor productivity growth rates will grow at the same rate c. An increase in the saving rate will lead to a smaller increase in the rate of per capita income growth for a country with a lower capital-output ratio than for a country with higher capital-output ratio d. An increase in the saving rate will lead to a bigger increase in the rate of per capita income growth for a country with a lower capital-labour ratio than for a country with a higher capital-labour ratio

Answer 1

Solution:

15. Formula of complete growth for such production function is:

GDP growth rate = TFP growth rate + 0.3*capital growth rate + 0.7*labor growth rate

0.05 = TFP growth rate + 0.3*0.02 + 0.7*0.02

TFP growth rate = 0.05 - 0.02 = 0.03 or 3%

So, correct option is (b) 3.0%.

16. Denoting alpha by a, for ease of writing. With constant A and doubled K and L, new production becomes:

Y' = A*(2K)^a*(2L)^1-a

Y' = A*2^a+(1-a)*K^aL^1-a

Y' = 2(A*K^a*L^1-a) = 2Y, so twice the old output.

Thus, correct option is (a) Double.