Given the production function Y = A , if the rental price of capital is 0.133, Y = 690, and K = 1,728, what is the value of the exponent ?? If A = 1, and the real wage is 1.15, is this economy in a long-run equilibrium?
What will be an ideal response?
Since the rental price of capital equals the marginal product of capital, we have 0.133 = , so α = one-third. If A = 1, we have 690 = 12 × , so L = 436. Then the real wage is = 1.06 ≠ 1.15. This is not a long-run equilibrium. Equivalently, if the equilibrium real wage is 1.15, L must satisfy 1.15 = , so L = 400. Then Y = 12 × = 651.3 ≠ 690. This is not a long-run equilibrium. (If the real wage remains 1.15, the quantity demanded of labor will fall to 400. Then, the excess supply of labor will force the real wage to decline to the market equilibrium value of 1.06.)
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