Question

Jamba Juice makes smoothies in a monopolistically competitive market. The inverse demand is: P = 8 – 0.05Q and MC = 2. a. To maximize profit, how many smoothies should Jamba make? b. What is the price? c. What is Jamba’s profit?

Answer 1

As per the question Jamba juice which makes smoothies in a monopolistically competitive market

Has the inverse demand function Average Revenue(AR) or P=8 -0.05q     and MC=2

Total Revenue (TR) = AR x q =( 8 -0.05q) = 8q – 0.05q²

Marginal Revenue (MR) =dTR/dq =8-0.1q

(A) at profit maximisation output MC should equal with MR

Þ MC = MR

Þ 2 = 8-0.1q

Þ 0.1q = 6

Þ q = 60

To maximise profit Jamba should make 60 units of smoothies

(B) Price at profit maximising unit

P=8 -0.05q     ( Replacing the value of Q=60)

P= 8 -0.05(60)

P =8 -3=5

The price at profit maximising output is 5

(C) Jamba’s Profit = Total Revenue(TR) - Total Cost(TC)

Total Revenue (TR) = 8q – 0.05q²

MC = 2

Total cost (TC) is the integration of MC

TC = Integration 2 dq = 2q

Profit = TR – TC

Profit = 8q – 0.05q² – 2q ( Replacing the value of Q=60)

Profit = 8(60) – 0.05(60)² – 2(60)

Profit = 480 – 180 – 120

Profit = 480 – 300 = 180

Jamba’s Profit is 180