Problem 2

```Problem 2 of MIDTERM
Page 279 #14
Group 6
Ritchie Roi Chua
Ramon Jose Miguel Naguiat
Mary Jane L. Paglumotan
Mark Anthony Salazar
Charlotte Tang
Tong Ya(Nicole)
Problem 2 (Page 279 # 14)

In the demand function given, a point is
specified with one given coordinate
A. Find the value of the other coordinate
B. Find the coordinates of the new point corresponding
to the changed (increased or decreased) price or
demand level
C. Approximate the price elasticity of demand at the
specified (first) point, using the results of (a) and (b)
D. Find the arc price elasticity of demand at the
specified point. Classify and interpret this result
5
X= (36-P2), P=2, price increase by 1 (monetary) unit
4
Solution
A.
VALUE OF X
X=(5/4)(36-P2)
P=2
X=(5/4)(36-4)
X=40
B.
When price increases by 1 monetary unit :
P=2+1=3
X=(5/4)(36-P2)
X=(5/4)(36-9)
X=33.75
Solution
C.
Price Elasticity of demand at P=2
ΔX = 33.75-40
= - 6.25
ΔP=3-2
=1
η=EX/EP= (P/X)(ΔX/ΔP)
η= (2/40)(-6.25/1)
η= -0.3125
Solution
D.
The arc price elasticity of demand
between the points is :
η=EX/EP=[(3+2)/(33.75+40)]*(-6.25/1)
=(5/73.75)*(-6.25/1)
= - 0.37
Solution
E.
Exact elasticity of demand at P=2
E = EX/EP = (P/X)*(dx/dp)
To get dx/dp:
X = (5/4)(36-P2)
dx/dp =(5/4)(-2P)
dx/dp = - 5p/2
E=EX/EP= (P/X)*(dx/dp)
=(P/X)*(-5p/2)
At P=2, X=40 :
E=(EX/EP)=(2/40)*(-10/2)
= -1/4
Conclusion: A 4% increase in price is expected to
decrease demand for the commodity by 1%, when the
prevailing price is Php2 and the corresponding
demand is 40 units
Graph
X=(5/4)(36-P2)