Answer:
a.–7.5% or -0.075
bi.$35,321
bii.$8,271
biii.$27,050
Explanation:
Wyandotte Chemical Company
a.
ED = %ΔQD / %ΔP
–2.0 = 15% / %ΔP. (15% more sales)
%ΔP = 15% / -2.0
%ΔP = –7.5% or -0.075
b.
Using the arc price formula, the new price will be:
%ΔP = P2 – P1/ [(P2+ P1)/2]
–0.075 = (P2– 15.00)/ [(P2+ 15)/2] -0.075P2– 1.125 = 2P2– 30
-2.075P2= -28.875
P2= $13.92
ΔP = $15 –$13.92 = $1.08
Finding new quantity using the arc price formula:
%ΔQ = Q2 – Q1/ [(Q2+ Q1)/2]
0.15 = (Q2– 30,000)/ [(Q2+ 30,000)/2]
Q2= 34,865 gallons (QUANTITY SOLD)
Therefore impact of the price cut on the following are:
i). On Total Revenue:
TR = P · Q
Before cut price: TR1, = 15(30,000) = $450,000
After cut price: TR2= 13.92(34,865)
= $485,321,
Consequently, ΔTR = $35,321 (change in total revenue)
ii). On Total Cost: we first find the FC and VCBefore price cut:
FC1=$90,000
After price cut: FC2= $90,000
VC per unit = $6.00 – 0.60 = $5.40
VC2= $5.40 × 34,865 = $188,271
TC2= FC + VC = 90,000 + 188,271 = $278,271
ΔTC = $8,271 (change in total cost)
iii). On Total Profits (π):
Before price cut: π, = $450,000 – $270,000 = $180,000
After price cut: π2= $485,321 – $278,271 = $207,050
(ΔTR - ΔTC = Δπ: $35,321 - $8,271 = 27,050)
