Let P be the price of a stock. The investor wants to purchase Q units of this stock. Suppose investor’s equity is E and assume that equity is strictly smaller than the value of the stock investor wants to purchase. As such, the investor receives a loan, L from the broker.

Give a formula that expresses the margin M in terms of L, P, and Q

After the loan was made, suppose the price of the stock falls to λP, where 0 < λ < 1. Find the new margin, in terms of M and λ.

Now let the maintenance margin be c, where 0 < c < 1. Find the largest λ, call it λ∗ such that, given our initial margin M and maintenance margin c, whenever λ > λ∗ the broker will not issue a margin call.