Integration Analysis - Math Problem Example

For example, if customers only demand (or can access) 5 units, they will be willing to pay 51- 52 = £26 (according to market demand, but according to the market supply and demand the market price remains at £15, hence consumers save (26-15 = £11), for the fifth unit bought. The £11 is thus the consumer surplus. It increases as the quantity demanded decreases.

Producer surplus on the other hand is the gain to producers for every unit of quantity supplied below the optimal quantity because the equilibrium price exceeds the price at which suppliers are willing and able to supply that quantity.  According to the case above, producers are willing to supply 3 units for £ 8.25 ( 6+ 32/4 ), but the market price gives them an advantage of (15-8.25 = £6.75) for the third unit sold. The excess is the producer surplus, which reduces as the quantity produces approaches the equilibrium quantity.

To obtain the indefinite integral, multiply the first u with the second dv and so on, and either get the sum by making use of the signs in the last column.

As observed in (ii) above the peak rate is at 5 from which the rate starts decreasing. Therefore as t approaches infinity (moves away from 5), then the rate approaches zero.  This trend explains the large negative difference between the totals of the two periods.

Typically, consumer surplus is the area under the demand curve but above the equilibrium price.  While producer surplus is the area above the supply curve limited by the horizontal line at the equilibrium price as shown in the diagram.

Note that in this case, producer surplus exceeds consumer surplus contrary to what was observed in question two. Probably, the producers can restrict supply and hence push price high (towards the demand curve) hence reducing the gain to consumers.