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Country A and country B both have the production function

Y = F(K, L) = K1/2L1/2.

Does this production function have constant returns to scale?

Yes, the production function has constant returns to scale. We can see this because when we increase labor and capital by the same proportion, output also increases by the same proportion. In other words, if we multiply capital and labor by the same factor, z, in the production function, K1/2L1/2, we obtain zY for output.

What is the per‑worker production function, y = f(k)?

The per-worker production function is _______.

Review pages 60-62 in Chapter 3 for a discussion of the Cobb-Douglas production function and returns to scale and then Chapter 7 for a discussion of the per-worker production function.
Review pages 60-62 in Chapter 3 for a discussion of the Cobb-Douglas production function and returns to scale and then Chapter 7 for a discussion of the per-worker production function.
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      Country A and country B both have the production function

      Y = F(K, L) = K1/2L1/2.

      Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker.

      Country A:

      k* =

      y* =

      c* =

      Country B:

      k* =

      y* =

      c* =

      Review section 7-1 for a discussion of steady-state equilibrium in the Solow growth model.
      Review section 7-1 for a discussion of steady-state equilibrium in the Solow growth model.
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          Country A and country B both have the production function

          Y = F(K, L) = K1/2L1/2.

          Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Round your answers to two decimal places.

          Country A:

          y =

          c =

          Country B:

          y =

          c =

          Review text pages 218-229 and Table 7-2 for a discussion of capital accumulation in the Solow growth model and details of how the economy adjusts to its steady state.

          Review text pages 218-229 and Table 7-2 for a discussion of capital accumulation in the Solow growth model and details of how the economy adjusts to its steady state.

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