Consider an economy with a saving rate 𝑠 ¯ = 0.3 , a depreciation rate 𝑑 ¯ = 0.1 , and a population growth rate 𝑛 ¯ = 0.03 . TFP is 𝐴 ¯ = 6  and the capital income share is 𝛼 = 0.35 . You know that the capital-labor ratio currently grows at a rate of 8.5 percent, i.e. Δ 𝑘 𝑡 + 1 𝑘 𝑡 = 0.085 . What is the capital-labor ratio 𝑘 𝑡 ? Round your answer to the nearest tenth.数值题

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Consider two countries, labeled 1 and 2. Each has the production function 𝑌 𝑖 = 𝐴 ¯ 𝑖 𝐾 𝑖 𝛼 𝐿 𝑖 1 − 𝛼 , for i = 1, 2. Assume that the countries currently have the same GDP per person, 𝐾 1 = 𝐾 2 , common saving, population growth, and depreciation rates, and 𝐿 1 < 𝐿 2 . Based on this information you know that, in the long run, GDP per capita in country 1 ( 𝑦 1 ) is _______   𝑦 2 . Hint: Based on the information above, what do you know about 𝐴 1 relative to 𝐴 2 ?

If, in addition, the economy's population grows at rate  𝑛 , i.e., 𝐿 𝑡 + 1 = ( 1 + 𝑛 ) 𝐿 𝑡 , you know that the steady-state capital-labor ratio is ________.

Using the Solow model, if, at time t = 0, the initial capital stock is 𝐾 0 = 500 , investment is 𝐼 0 = 240 , and δ = 0.12  is the depreciation rate, capital accumulation from period 0 to period 1 (i.e., Δ 𝐾 1 ) is:

Consider an economy with a saving rate 𝑠 ¯ = 0.2 , a depreciation rate 𝑑 ¯ = 0.1 , and a population growth rate 𝑛 ¯ = 0.025 . TFP is 𝐴 ¯ = 8 and the capital income share is 𝛼 = 0.36 . You know that the capital-labor ratio currently grows at a rate of 7.5 percent, i.e., Δ 𝑘 𝑡 + 1 𝑘 𝑡 = 0.075 . What is the capital-labor ratio 𝑘 𝑡 ? Round your answer to the nearest tenth.

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