Answer :
Turkey's MPK relative to the United States is approximately 0.851, indicating that Turkey's capital is less productive than that of the United States in terms of generating additional output per worker.
Turkey's MPK relative to the United States can be calculated by comparing their output per worker and capital per worker. Given the production function q = Ak^(1/3), where q represents output per worker and k represents capital per worker, the relative MPK of Turkey can be determined.
The marginal product of capital (MPK) measures the additional output generated by an additional unit of capital. In this case, we are comparing Turkey and the United States, which have different output per worker and capital per worker. The production function q = Ak^(1/3) implies that the output per worker (q) is equal to the total factor productivity (A) multiplied by the capital per worker (k) raised to the power of 1/3.
Given that the United States has an output per worker of 1 and capital per worker of 1, we can substitute these values into the production function to find the value of A. Using the equation 1 = A * 1^(1/3), we find that A = 1.
Similarly, for Turkey, with an output per worker of 0.32 and capital per worker of 0.24, we can substitute these values into the production function to find A. Using the equation 0.32 = A * 0.24^(1/3), we can solve for A, which is approximately 0.676.
Now, to find the relative MPK of Turkey relative to the United States, we compare their capital per worker ratios. Turkey's capital per worker is 0.24, while the United States' capital per worker is 1.
By dividing Turkey's A by the United States' A and raising it to the power of 1/3, we get (0.676/1)^(1/3), which is approximately 0.851.
Therefore, Turkey's MPK relative to the United States is approximately 0.851, indicating that Turkey's capital is less productive than that of the United States in terms of generating additional output per worker.
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