Could you please derive the following. Or even your best attempt if you cannot do.

Derive the following equations presented in the lecture on monopsony power in labor markets: 1. The probability of worker i choosing firm j: P (arg max{uij, uib} = j) = exp (B log wj) exp b + EKEJM exp (B log Wk) 2. The labor demand of firm j: p B log , = B B+1 log + B+1 [log N + log AM ] log WM = 1 B 1 log p B+ 1 wj B + 1/ B + 1 [log N + log 2M] 3. The labor demand of firm j that paid below the minimum wage before the introduction of the minimum wage and that, conditional on not exiting the market in response to this policy change, pays the minimum wage after its introduction: WMW log LAW = - log ; - log WMOne type of labor, low skilled. Worker i's indirect utility in firm j: uij = Blogwj + eij if employed; w;: wage Wib = b + cib if non-employed; b: benefit Idiosyncratic preferences: Eij, Eid, drawn from type I extreme value distribution. Workers choose firm that provides highest utility, so that P (arg max (uij, Wib} = j) exp(B log wj) exp b + 2KEIM exp (B log Wk) = AM exp( log w;) JM: firms that enter market under monopsonistic competition AM : same in every firm