The price changes triggered by a market order depend on the content the limit order book.
A lob with constant depth yields a price change which is linear in the order size.
A lob with linearly increasing depth yields a price change which is grows as the square root of the order size.
A lob with quadratically increasing depth yields a price change which is grows as the cubic root of the order size.
A lob with constant depth yields a price change which is linear in the order size.
And so on. . The code is here. Among the empirical values reported in the literature for the function's exponent I've found 0.5 and 0.76.
