Consumer surplus and producer surplus

Note: Under DSE syb. the concept of “benefit” is used, equivalent to “used value” or “utility” in AL or other textbooks.
Exchange theorem: people exchange only if the benefit is greater than the equilibrium price.
Benefit = Max. willingness to pay/ max. demand-price of a good
TB = benefit of consuming a given quantity of good. = ΣMB, MBn=TBn-TBn-1
It’s assumed that MB is strictly decreasing.
TC = Least money to produce the good / min. supply-price of a good, MCn=TCn-TCn-1=TVCn-TVCn-1, note that TC=TVC+TFC=TFC+ΣMC.
MC curve = Supply curve since cost of producing an additional unit is the minimum selling price, similarly MB curve = demand curve.
Consumer surplus (CS) is consumer’s gain from market exchange. It’s the extra amount that the consumer is willing pay more than he actually pays. Mathematically,
CS = TB-TE = ΣMB-PQ = Σ(MB-P). In the graph, we consider the area between P and MB. Continuity of the curve is considered. CS maximized as MB=P.
Producer surplus (PS) = producer’s gain from market exchange. It’s the extra amount that a producer actually receive above the min. amount he must receive. Mathematically,
PS = TR-TVC = PQ-ΣMC = Σ(P-MC)   (Note: PS is different from profit P = TR-TC, so that PS = P + TFC) In the graph it’s the area enclosed by P-axis, MC curve and P curve.
PS is maximized as MC = P.
Social surplus is the total gain from market exchange for consumers and producers (as well as third party if necessary).
MSS=MB-MC, TSS=ΣMSS=CS+PS. When MB>MC, MSS for additional unit>0, therefore it’s under-produced. Oppositely MC>MB implies MSS<0 for additional unit, then it’ll be overproduced. Therefore MC=P=MB implies equilibrium and maximization of TSS.
For when the curve shifts in parallel manner, CS/PS/TSS changes in the same manner as the equilibrium quantity changes. i.e., if Q increases, CS/PS/TSS increases.