1. Given production function $F(L, K) = L^\alpha K^\beta$, where $\alpha + \beta = 0.9$; we use $p$ for the price of production goods, $w$ for the wage and $\rho$ for the price of capital. In the short run, $K = \bar{K}$, capital is fixed. solve $L^*$ in terms of $(p, w, \rho, \bar{K})$.