Question

Here again is the quick review of some algebraic properties of exponents:  ka *kb = ka + b  ka *k-b = ka – b  k-b = 1/kb  ka /kb = ka – b  k1/2 = k  If k1/2 = a then k = a2  (k*g)a = ka *ga  ka /ga = (k/g)a

Questions 1-8 and A use the following information. Suppose an economy with a capital-output ratio (K/Y) is about 2.5; an average growth rate of GDP of about 3% per year and a depreciation rate (δ) is about 5% per year. Also, suppose that this economy is at its steady state.

1. If K/Y = 2.5, then k/y equals (a) 2.5 (b) 4 (c) 5 (d) Cannot be determined; we need values for the labor force (L) and the efficiency of labor (E)

2. The value for the sum of the parameters n + g at the steady state is (a) 2.5 (b) 0.03 (c) 0.03% (d) Cannot be determined, we need the rate of growth of population (n) and the rate of growth of labor productivity (g), which are not given

3. The saving rate is [HINT: Use the steady-state condition sy = (δ + n + g)k and solve for s] (a) 0.032 (b) 0.225 (c) 0.175 (d) 0.2

4. The growth rate of output per effective worker (Y/LE) at the steady state is (a) 0 (b) 3% (c) 5% (d) 8% 2

5. The growth rate of output per worker (Y/L) at the steady state is [HINT: What the growth rate of Y? What about for L? Use the properties of growth rates for fractions discussed in class] (a) 0 (b) 3% (c) 5% (d) Cannot be determined; we need the value for g

Suppose that the economy presents the following production function: α y  f(k)  k where α corresponds to the capital share in GDP and is a positive constant. In this case, the marginal product of capital (MPK) is constant at the steady state and equals MPK = αY/K

6. Suppose that α = 0.3. Would the economy be at its Golden Rule steady state? [HINT: Recall that we’re using K/Y = 2.5 and that K/Y is the inverse of Y/K] (a) Yes, MPK = δ + n + g (b) No, MPK > δ + n + g (c) No, MPK < δ + n + g (d) Cannot be determined with the information provided

7. What is the capital-output ratio (K/Y) that is consistent with the Golden Rule steady state? [HINT: Use the definition MPK = αY/K and what MPK should be equal to at the Golden Rule] (a) 3.75 (b) 0.266 (c) 2.5 (d) 4.286

8. Using the Golden Rule K/Y ratio you found in question 7, find the saving rate that would be necessary for the U.S. economy to reach the Golden Rule steady state (sgold) [HINT: Use the steady-state condition sy = (δ + n + g)k and solve for s] (a) 0.021 (b) 0.2 (c) 0.3 (d) 0.225

Answer 1

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