Let a firm produce $Q'$ amount of good, less than the optimal amount. But if it produces more, it can increase the profits (because at $Q'$, MR> MC).

Now consider a firm producing $Q''$ amount of good, higher than the optimal amount. They will tend to produce less because at $Q''$, MC > MR.

This tends to move the firm to produce amount $Q$, where MR=MC. This is the intuitive answer to why profit maximisation occurs at $\text{MR=MC}$.

Demand-Supply

The demand and supply curve can be plotted together. Supply curve in increasing and demand curve is decreasing with quantity. The intersection of these two curves is the market price.

When there are excess profits, new firms join the market. This causes a rightward shift in the supply curve. This shifts the intersection of demand and supply curves and shifts the market price, bringing it down. The price adjustment continues till the excess profits is elminated. The firms then earn only normal profits.

When there is loss, firms leave the market, causing the supply curve to shift left, resulting in a new equilibrium at a higher price. Here too, the price adjustment continues till the loss is removed. In the long run, firms earn only normal profit.

Income increase

What happens when the consumer income increases? Demand curve shifts rightward, resulting in a new, higher price.

What if this new price results in excess profits for the firms? New firms enter the market, supply curve shifts right, and the firms return to earning normal profits.

Consumer's surplus

Different consumers are willing to pay different amounts for the same good. But all the buyers buy the good at the same price, which is the market price. The amount saved by the consumers is called consumer's surplus. In the supply-demand curve, this is the area above the market price $P$ and below the demand curve.

Producers surplus

There are some suppliers willing to sell at lower prices than the market price. But they all sell at market price. This additional amount is called producers surplus. Graphically, it is the area below the market price and below the supply curve in the supply-demand curve.

In perfectly competitive markets, the consumer's surplus belongs with the consumers and producers surplus belongs to the producers.