Question 2

Question 2 (a) Demand

P = 3000 - Q

Fix cost = $250,000 per month Variable cost (C) = 1000 per unit x

quantity (Q)

= 1000Q Total cost per unit (TC) = variable cost + fix cost = 1000 Q + $250,000 per month

Revenue(R) = price(P) x quantity(Q) = (3000 – Q) x Q = 3000Q - Q2 Profit = R - TC = ( 3000Q - Q2 ) - 1000Q + $250,000 = 3000Q - Q2 - 1000Q - $250,000 = 2000Q - Q2 - $250,000

Profit’ = 2000 – 2Q If, Profit’ = 0 2000 – 2Q = 0 -2Q = 0 Q = 1000 units Profit “ = -2 < 0 (maximum) Let say,

Q = 1000 units

Demand Q

P = 3000 -

Let say, Q = 1000units = 2000(1000unit)- (1000unit)2 - $250,000 P = 3000 – Q = $ 750,000

Profit = 2000Q - Q2 - $250,000

b)

Demand

P = 3000 - Q - 500

P = 2500 – Q Revenue(R) = price(P) x quantity(Q) = 2500Q x Q2 Total cost per unit (TC) = variable cost + fix cost = 1000 Q + $250,000 per month Profit = R – TC = 2500Q - Q2 - 1000Q - $250,000 = 1500Q - Q2 Profit’ = 1500 - 2Q If , 0

Profit’ = 0

= 1500 - 2Q -2Q = -1500 Q = 750 Profit “ = -2 < 0 (max)

Profit = 1500Q - Q2 Let say, Q = 750 units = 1500(750units) – (750 units) 2 = $562500 Yes, it is a profit-maximizing strategy because it still remain the maximum Profit “ = -2 < 0

d) Demand

P = 2,800 – 2Q

Revenue(R) = price(P) x quantity(Q) = 2800Q - 2Q2 Total cost per unit (TC) = variable cost + fix cost = 1000 Q + $250,000 per month Profit = R – TC = 2800Q - 2Q2 - 1000 Q - $250,000 = 1800Q - $250,000 - 2Q2 Profit ‘ = 1800 – 4Q Let say, Profit ‘ = 0 1800 – 4Q = 0

Demand – 2Q

Q = 450

P = 2,800

Let say Q = 450 units

Profit” = -4 < 0 (max)

P = 2,800 – 2(450 units)

Profit = R – TC

Price (P) = $1900

Let say, Q = 450 units = 1800Q - $250,000 - 2Q2 = 1800(450 units) - $250,000 – 2(450)2 = $155,000

Compare two choices Cutting price to sell the entire inventory If the price cut down $200 Demand P = 2,600 – 2 Q2 Revenue(R) =2600Q - 2Q2 Total cost per unit (TC) = 1000 Q + $250,000 Profit = R – TC = 26000Q - 2Q2 – 1000Q – 250000 = 1600Q - 2Q2 – 250000 Profit’ = 1600 – 4Q Let say , Profit’ = 0 0 = 1600 – 4Q

Maintaining the price in part a) Total Q (selling less then the total inventory) = 999units Total cost = 1000 Q + $250,000 per unit (TC) = 1000 (999units )+ $250,000 = $1,249,000 Price for question a) = $ 2000 per unit Total Revenue(R) = P x Q = $2000 x 999 unit = $1,998,000

Q = 400 units Profit” = -4 < 0 (max) Profit = 1600Q - 2Q2 – 250000 Let say, Q = 4000 units = 1600(4000units) 2(4000units)2 – 250000 = $70000

Total Profit = total revenue – total cost = $1,998,000 $1,249,000 = $ 749,000

Yes, I agree with the maintaining price manager. I will set $2000 per unit as the optimal price.