Suppose labor's share of GDP is 70 percent and capital's is 30 percent, real GDP is growing at a rate of 4 percent a year, the labor force is growing at 2 percent, and the capital stock is growing at 3 percent. What is the growth rate of total factor productivity?

The Cobb-Douglas production function, also known as the neoclassical growth model, relates the growth of the economy (real GDP) to the growth of its inputs (labor force and capital stock) and the growth of technology (total factor productivity). The general form of this function is: Y = A * K^α * L^(1-α) where: - Y represents Real GDP - A is Total Factor Productivity (TFP) - K is the capital stock - L is the labor force - α is the share of capital in GDP (0 ≤ α ≤ 1) - (1-α) is the share of labor in GDP In the context of growth rates, we can write the equation as: g_Y = g_A + α * g_K + (1-α) * g_L where: - g_Y is the growth rate of real GDP - g_A is the growth rate of total factor productivity (what we're trying to find) - g_K is the growth rate of capital stock - g_L is the growth rate of the labor force

Using the given values from the exercise, we can plug them into the modified Cobb-Douglas production function to determine the growth rate of total factor productivity: Share of labor (1-α) = 70%=0.7 Share of capital (α) = 30%=0.3 Real GDP growth rate (g_Y) = 4% Labor force growth rate (g_L) = 2% Capital stock growth rate (g_K) = 3% According to the growth equation: 4 = g_A + 0.3 * 3 + 0.7 * 2 Now, we can solve for the growth rate of TFP (g_A): g_A = 4 - [0.3 * 3 + 0.7 * 2] g_A = 4 - (0.9 + 1.4) g_A = 4 - 2.3 g_A = 1.7 The growth rate of total factor productivity is 1.7%.