B List of variables

This is just a short list of variables that are used in the text.

Remember that capital letters represent aggregates, lower case letters represent per-worker quantities, and a \(t\) subscript means at time \(t\) (e.g., \(x_t\) is the quantity of \(x\) in year \(t\).)

• \(Y_t\) - aggregate GDP
• \(L_t\) - Number of workers
• \(y_t\) - GDP per worker, \(Y_t / L_t\)
• \(K_t\) - aggregate stock of physical capital
• \(k_t\) - physical capital per worker, \(K_t / L_t\)
• \(H_t\) - Human capital
• \(h_t\) - human capital per worker, \(H_t / L_t\)
• \(A_t\) - Productivity (Note that we don’t think about ``productivity per worker.’’)
• \(I_t\) - Aggregate investment in physical capital
• \(i_t\) - Investment in physical capital per worker, \(I_t / L_t\)
• \(C_t\) - Aggregate consumption
• \(c_t\) - Consumption per worker, \(C_t / L_t\).
• \(Y_t = f (A_t, L_t, K_t, H_t)\) is the production function
• \(\gamma\) (lower-case Greek letter “gamma”) - The fraction of output that is invested in a period, \(I_t = \gamma Y_t\), \(0 < \gamma \leq 1\)
• \(\delta\) (lower-case Greek letter “delta”) - The fraction of the capital stock that wears out every period, \(0 < \delta \leq 1\). The total capital that wears out in a period is \(\delta K_t\).
• \(\alpha\) (lower case Greek letter “alpha”) - The exponent on physical capital in the Cobb-Douglas production function. \(0 < \alpha < 1\)