1.
P=16eβ0.02Q
Total revenue=TR=PQ=16eβ0.02Q.Q
Ξ΄QΞ΄TRβ=16eβ0.02Q+16Q(β0.02)eβ0.02Q=0
16eβ0.02Q[1β0.02Q]=0
[eβ0.02Q is always positive]
so, 1β0.02Q=0
Q=0.021β=50
P=16eβ0.02(50)
p=e16β=2.7216β=5.88
(b)
Ξ΄Q2Ξ΄2TRβ=16eβ0.02Q(β0.02)+(β0.032)eβ0.02Q
=β0.32Qeβ0.02(0.02)
<0
=negative
second order is also satisfied.
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