Now, let$s$ consider a model $of$ statistical discrimination. Suppose $we$ have a firm

who uses two labor inputs, $Lm-$ a male worker and $Lf-$ a female worker. The

firm$s$ profit $is$ defined $by$

$=pmLm+pfLf-wmLm-wfLf$

where $pmis$ productivity $of$ a male worker and $pfis$ productivity $of$ a female worker.

$wm$ and $wf$ are wage rates for a male and a female worker.

$(a).$ Write down the firm$s$ profit$-$maximizing wage for each male and female worker

$(b).$ Suppose the firm falsely believes that the distribution $ofpm$ has a mean equal

$to2\mathrm{.}6$ and the firm believes that distribution $ofpf$ has a mean equal $to2\mathrm{.}4.$

What will $be$ the profit$-$maximizing wage for each male and female worker?

$(c).$ Can $we$ distinguish this kind $of$ firm$s$ false belief $on$ a worker$s$ group average

with pure taste$-$driven discrimination? Criticize the statistical discrimination

model with your economic explanations.