In: Economics
1. The consumer’s demand for good X is described by the function x = 200 – 5Px, where x denotes the quantity of good X demanded and Px is the price (in euros) per unit of good X. Suppose that the price per unit of good x decreases from 30 euros to 20 euros. Calculate the change in the consumer’s (net) surplus that is associated with this price decrease of Y. Illustrate the change in the consumer surplus in the graph. Mark very clearly the area that corresponds to the change in the consumer’s (net) surplus and identify very clearly all the numerical values that are important for calculation of the change of consumer’s (net) surplus. (10 points)NB! Please note that the points from Exercise 1 will be added to the Homework 1 result, as informed earlier.
We have x = 200-5Px
We have two prices ie 30 euros and it decreased from 20 euros
At 30 euros the value of x is
x= 200- 5(30) = 200-150 = 50
at price = 20 euros
x = 200 -5(20) = 200-100= 100
Marking them on the graph , we get Px as 30 euros and Px' as 20 euros
Consumer surplus is given by the area between the demand curve and price line
The area of consumer surplus at price 30 euros is given by area ABC ie the triangle ( given in the figure )
area of traingle ABC = 1/2*B*h = 1/2*(40-30)*(50-0)
= 1/2*10*50= 250sq units
Area of consumer surplus at price 20 euros is given by area ADE ie triangle
Area of triangle ADE = 1/2*b*h =1/2*(40-20)*(100-0)
=1/2*(20)*100 = 1000 sq units
Change in the consumer surplus ie area of triangle ADE- area of triangle ABC
= 1000-250 = 750 sq units = area of shaded region (BDEC)
So the change in consumer surplus when the price changes is area of BDEC given by $750
(You can comment for doubts )