¿How does the model from “Noise trader risk in finantial markets” paper work?

Question

I have been struggling in understanding how the author of this paper got to his conclusions. I uploaded an image of a fragment of this paper. The model is a simple 2 agent, a sophisticated investor and a noise trader. Each agent lives 2 periods (young and old). They spent their entire wealth (exogenous) when young to maximize their wealth when old. The only decision they make is how much of the risky asset should they buy and how much of the risk less asset. Both assets are identical except the risky asset supply is fixed and the riskless asset supply is unlimited. The riskless asset price is set to 1 and the risky asset price is Pt. Both agents maximize a negative exponential CARA utility function, as shown in the image.
The idea is that sophisticated investors choose how much of the risky asset to buy in the first period depending on their expectation of the price in the second period. This expectation is normally distributed. The unsophisticated investor faces the same decision only it miss perceives the expected price of the riskless asset. I understand why the author chose a CARA function but what I cannot understand is how he went from equation 2 in the image to equation 3 and from 3 to 4. I do not understand why maximizing the expected value of 2 is equal to maximizing the expected value of 3 and I don’t understand how that became equation 4. I really need some help with this. I appreciate the help