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1. Suppose an economy described by the Solow capital share of a third, a saving rate of 24 percent, model has the following production function:

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1. Suppose an economy described by the Solow capital share of a third, a saving rate of 24 percent, model has the following production function: a depreciation rate of 3 percent, a rate of popula- tion growth of 2 percent, and a rate of labor- Y = K'/2(LE) 1/2. augmenting technological change of 1 percent. It is in steady state. a. For this economy, what is /()? b. Use your answer to part (a) to solve for the a. At what rates do total output, output per worker, and output per effective worker grow? steady-state value of y as a function of s, n, g. and 6. b. Solve for capital per effective worker, out- put per effective worker, and the marginal c. Two neighboring economies have the above product of capital. production function, but they have different parameter values. Atlantis has a saving rate c. Does the economy have more or less capital of 28 percent and a population growth rate than at the Golden Rule steady state? How of 1 percent per year. Xanadu has a saving do you know? To achieve the Golden Rule rate of 10 percent and a population growth steady state, does the saving rate need to rate of 4 percent per year. In both countries, increase or decrease? ! = 0.02 and 6 = 0.04. Find the steady-state d. Suppose the change in the saving rate you value of y for each country. described in part (c) occurs. During the 2. LaunchPad . An economy has a Cobb-Douglas transition to the Golden Rule steady state, will the growth rate of output per worker be production function: higher or lower than the rate you derived in Y = K"(LE) 1-a. part (a)? After the economy reaches its new steady state, will the growth rate of output (For a review of the Cobb-Douglas production per worker be higher or lower than the rate function, see Chapter 3.) The economy has a you derived in part (a)? Explain your answers

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