Questions attached below:

'l. The country of A has the following production function: Y : K05 \"15 Where: '1" is output, K is capital stock, L the number of workers Questions: I]. 1"-I""iI"rite down the production function in the form of output per worker. Show that the production function has the properties of: {i} constant return to scale and {ii} diminishing return with the increase of capital stock per worker. The country of B has exactly the same production function as A's. l{Currently the amount of capital stock per worker in A is higher than B, ceteris paribus. What is your prediction about the economic growth rate in A compared to B? Explain your answer using the graph for capital and output dynamics lhint: capital per worker on the X axis, output per worker on the '1" axis]. Assuming in A, the saving rate {s} is 0.32;. depreciation rate [5] is 0.03. Calculate the steady state levels of capital accumulation, output, investment and consumption per worker. 1"-I""iI"ill the current saving rate of A create the optimal steady state consumption level? Explain your answer [hint: find the derivative of the equation of consumption per worker in steady state with respect to the saving rate}. Assume that the saving rate {s} suddenly increases to 0.5, what will the dynamic evolution of output per worker look like? [hint: draw the graph that shows the dynamic of output per worker over time when the saving rate {s} change, you do not have to be precise with the magnitude]