Calculate the level of productivity a in each country

Question

ECON 448: Week 7-

1. Development Accounting and Growth Accounting

1. Development accounting is about the income difference across countries at a given time, while growth accounting is about the income growth within a country over time.

2. Both method is useful to investigate where the income difference/growth comes from: Factor accumulation? Total factor productivity(TFP)?

Development Accounting:

y₁/y₂ = (A₁/A₂)(k₁^α1 h₁^1-α1/k₂^α2 k₂^1-α2)

Grwoth Accounting: (CRS Production Function)

g_y = g_A + αg_k + (1 - α)g_h

(α is the ratio of capital income to the total income)

3. Consider the following data on the fictional countries of Sylvania and Freedonia. The production function is y = Ak^αh^1-α, where α = 0.5.

	Sylvania	Freedonia
y (output per worker)	100	200
k (physical capital per worker)	100	100
h (human capital per worker)	25	64

(a) Calculate the level of productivity, A, in each country.

(b) Calculate the countries' relative levels of output if all differences in output were due to productivity.

(c) Calculate the countries' relative levels of output if all differences in output were due to factor accumulation.

4. The economy of Wonderland produces magic potions using capital (K) and labor (L). Total output is growing at the rate of 5 percent per year. The rental rate per unit of capital is 0.1 bottles of magic portion. The physical capital-output ratio is 3:1. The stocks of capital and population are growing at the rate of 3 and 2% respectively. Assume that everybody works.

(a) If all output is paid in wages and rent, calculate the shares of capital and labor in national income.

(b) Estimate the rate of technical progress (or TFP growth in Wonderland).

2. Inequality Measures

1. The Lorenz criterion: if the Lorenz curve of a distribution lies at every point to the right of the Lorenz curve of some other distribution, the former should be judged to be more unequal than the latter.

2. What if the Lorenz curves cross each other? Then we use several measures and compare them.

The Coefficient of Variation:

C = 1/µ√(_j=1∑^mn_j/n(y_j - µ)²)

The Gini Coefficient:

G = 1/2n²µ _j=1∑^m_k=1∑^mn_jn_k|y_j - y_k|

3. Draw Lorenz curves and calculate the Gini coefficient and the coefficient of variation for the income distributions (a)-(b).

(a) y_j: (100, 200, 300, 400), n_j: (50, 25, 75, 25)

(b) y_j: (100, 200, 300, 400), n_j: (50, 15, 95, 15).