Euclid preparation: V. Predicted yield of redshift 7<z<9 quasars from
  the wide survey
  We provide predictions of the yield of $7<z<9$ quasars from the Euclid wide
survey, updating the calculation presented in the Euclid Red Book in several
ways. We account for revisions to the Euclid near-infrared filter wavelengths;
we adopt steeper rates of decline of the quasar luminosity function (QLF;
$\Phi$) with redshift, $\Phi\propto10^{k(z-6)}$, $k=-0.72$, and a further
steeper rate of decline, $k=-0.92$; we use better models of the contaminating
populations (MLT dwarfs and compact early-type galaxies); and we use an
improved Bayesian selection method, compared to the colour cuts used for the
Red Book calculation, allowing the identification of fainter quasars, down to
$J_{AB}\sim23$. Quasars at $z>8$ may be selected from Euclid $OYJH$ photometry
alone, but selection over the redshift interval $7<z<8$ is greatly improved by
the addition of $z$-band data from, e.g., Pan-STARRS and LSST. We calculate
predicted quasar yields for the assumed values of the rate of decline of the
QLF beyond $z=6$. For the case that the decline of the QLF accelerates beyond
$z=6$, with $k=-0.92$, Euclid should nevertheless find over 100 quasars with
$7.0<z<7.5$, and $\sim25$ quasars beyond the current record of $z=7.5$,
including $\sim8$ beyond $z=8.0$. The first Euclid quasars at $z>7.5$ should be
found in the DR1 data release, expected in 2024. It will be possible to
determine the bright-end slope of the QLF, $7<z<8$, $M_{1450}<-25$, using 8m
class telescopes to confirm candidates, but follow-up with JWST or E-ELT will
be required to measure the faint-end slope. Contamination of the candidate
lists is predicted to be modest even at $J_{AB}\sim23$. The precision with
which $k$ can be determined over $7<z<8$ depends on the value of $k$, but
assuming $k=-0.72$ it can be measured to a 1 sigma uncertainty of 0.07.
