In the current Dark Energy Spectroscopic Instrument (DESI) survey, emission line galaxies (ELGs) and luminous red galaxies (LRGs) are essential for mapping the dark matter distribution at $z \sim 1$. We measure the auto and cross correlation functions of ELGs and LRGs at $0.80.1$ $\mathrm{Mpc}\,h^{-1}$. We can also reproduce the auto correlations of ELGs at $r_{\mathrm{p}}>0.3$ $\mathrm{Mpc}\,h^{-1}$ ($s>1$ $\mathrm{Mpc}\,h^{-1}$) in real (redshift) space. Although our model has only seven parameters, we show that it can be extended to higher redshifts and reproduces the observed auto correlations of ELGs in the whole range of $0.8Comment: 27 pages, 16 figures, accepted by ApJ