Solution assignment 04 Area and volume

Assignment 4

Calculate the area which is enclosed by the lines $Q=0$ and $P=20$ and the graph of the function $P=\displaystyle\frac{100}{Q+2}$ .
This assignment is relevant for the calculation of the Producer Surplus (see Bradley T. en Patton P., Essential Mathematics for Economics and Business, 2e ed., John Wiley, p. 416).

Solution

The intersection point of the graph of the function $P=\displaystyle\frac{100}{Q+2}$ and the line $P=20$ is $Q=3$ . Thus the area equals the area enclosed by the graph of $P=\displaystyle\frac{100}{Q+2}$ , $Q=0$ and $Q=3$ , minus the area of the rectangle through the points $(0,20)$ and $(3,0)$ .
Then we get:

$\displaystyle\int_{0}^{3}\frac{100}{Q+2}dQ-20\cdot3=100[\ln(Q+2)]_{0}^{3}-60=$

$=100(\ln(5)-\ln(2))-60=31.6291$

Return to Assignments Area and volume

Assignments

Solution assignment 04 Area and volume

Assignment 4

Solution

Contact

Tutor Math, Statistics or GMAT?

Language preference