Question

Consider an economy in a steady state with population growth rate η, a rate of capital depreciation δ , and a rate of technological progress g.

a)  At the steady state Δk = 0, where k equals capital per effective worker. What condition must be met for this to hold? Describe the condition in words as well as mathematical expressions.

b) Describe in words what is maximized at the Golden Rule level of k.

c) What mathematical condition must be met at the Golden Rule level of k?

d) Suppose that the production function is Y = 12K^1/3(EL)^2/3and capital lasts for an average of 10 years so that 10% of capital wears out every year (depreciate rate = 1/10 = 0.1 or 10%). Assume that the rate of growth of population is 4 percent, and the rate of technological growth is 2 percent.

            1. Derive the equation for output per effective worker y = Y/ (EL) = f(k).

            2. Calculate the Golden Rule level of capital per effective worker and the saving rate associated with this steady state. (Hint: First Derive the MP_k)

            3. ( Calculate all of the following at their Golden rule levels: output per effective worker, saving and investment per effective worker, and consumption per effective worker.

Answer 1

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