Consider the economy of Avataria, which can be described by the Solow model. Avataria has the depreciation rate of 6% and the production function Y(K,L) = ll.5*(K)3'4(L)\"'. (a) (10 points]. Prove that the production function in Avataria exhibits the constant return to scale property. (13) (15 points]. Assume that Avataria has the investment rate of 24%. Calculate the steady-state capital-labor ratio, output per worker. and consumption per worker. Also, what is the growth rate of the total (aggregate) output in Avataria in the steady state? (c) (15 points). Now assume that Avataria has the new investment rate, which increases its steady state output per worker by 40%. Calculate this new investment rate. (d) (15 points). Finally, assume that Avataria has the old investment rate of 24% but now its producers rely on capital relatively less so that the production function is Y{K,L) = 0.5(K)\"1(L )1\". How does this change affect output per capita in steady state compared to part (b)? Calculate its exact value and discuss the change