Question

Wyandotte Chemical Company sells various chemicals to the automobile industry. Wyandotte currently sells 30,000 gallons of polyol per year at an average price of $15 per gallon. Fixed costs of manufacturing polyol are $90,000 per year and total variable costs equal $180,000. The operations research department has estimated that a 15 percent increase in output would not affect fixed costs but would reduce average variable costs by 60 cents per gallon. The marketing department has estimated the arc elasticity of demand for polyol to be -2.0.

a. how much would Wyandotte have to reduce the price of polyol to achieve a 15 percent increase in the quality sold?
b. evaluate the impact of such a price cut on

(i) total revenue.
(ii) total costs, and
(iii) total profits.

Answer 1

a.–7.5% or -0.075

bi.$35,321

bii.$8,271

biii.$27,050

Step-by-step 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)