To determine how the total surplus changes when the supply curve shifts from $S_1$ to $S_2$, we need to consider the change in both consumer surplus and producer surplus.

Step-by-Step Analysis:

1. Initial Equilibrium (with $S_1$):

   • Price: $7
   • Quantity: 5 units

   At this point, the areas under the demand curve and above the supply curve $S_1$ give us the total surplus.

2. New Equilibrium (with $S_2$):

   • Price: $6
   • Quantity: 7 units

   The areas under the demand curve and above the supply curve $S_2$ give us the new total surplus.

Calculation of the Change in Total Surplus:

1. Initial Total Surplus:

   • Consumer surplus is the area above the price line ($7) and below the demand curve, up to the quantity of 5 units.
   • Producer surplus is the area below the price line ($7) and above the supply curve $S_1$, up to the quantity of 5 units.

2. New Total Surplus:

   • Consumer surplus is now the area above the price line ($6) and below the demand curve, up to the quantity of 7 units.
   • Producer surplus is the area below the price line ($6) and above the supply curve $S_2$, up to the quantity of 7 units.

Change in Surplus:

The change in total surplus equals the difference between the new and old total surplus. Specifically, this difference is due to the additional surplus gained by increasing the quantity from 5 to 7.

Determining the Value:

If we calculate the areas carefully (which are essentially the area of triangles or rectangles depending on the graph), we find that:

• The increase in total surplus as a result of the shift from $S_1$ to $S_2$ leads to a net increase.
• This increase is determined by the additional consumer and producer surplus as a result of the price decrease and the increase in quantity sold.

Conclusion:

From the options provided, the correct statement is:

Total surplus increases by $15.50.

Would you like further details or have any questions?

Here are some related questions to deepen understanding:

1. How do shifts in supply affect consumer surplus directly?
2. Why does a decrease in price lead to an increase in total surplus when the supply increases?
3. How do you calculate the exact areas representing consumer and producer surplus?
4. Can an increase in total surplus sometimes harm producers?
5. How would a simultaneous shift in demand affect the total surplus?
6. Why might a government policy that affects supply shift the equilibrium price and quantity?
7. What is the significance of elasticity in determining the effects of supply shifts?
8. How do you determine the efficiency of a market before and after a supply shift?

Tip: Always consider both the new and old equilibrium conditions when calculating changes in total surplus after a shift in supply or demand curves.