An industrial production process costs C(q) million dollars to produce q million units; these units then sell for R(q) million dollars.
If C(2.1)=5.2, R(2.1)=6.9 , MC(2.1)=.5 , and MR(2.1)=.6 , calculate the following.
( c= costs, r = revenue, MC = marginal costs, mr = marginal revenue)
(a) The profit earned by producing 2.1 million units.
The profit is 1.8 million dollars. ( This is an easy one, we figured out how to do it)
(b) The approximate change in revenue if production increases from 2.1 to 2.13 million units.
The change in revenue is about _____ thousand dollars.
(c) The approximate change in revenue if production decreases from 2.1 to 2.07 million units.
The change in revenue is about ______ thousand dollars.
(d) The approximate change in profit in parts (b) and (c).
The change in profit in part (b) is about ____ dollars, and the change in profit in part (c) is about ____ dollars.
If it helps, MC = C'(q), MR = R'(q), and profit = Total Revenue - Total Costs
If C(2.1)=5.2, R(2.1)=6.9 , MC(2.1)=.5 , and MR(2.1)=.6 , calculate the following.
( c= costs, r = revenue, MC = marginal costs, mr = marginal revenue)
(a) The profit earned by producing 2.1 million units.
The profit is 1.8 million dollars. ( This is an easy one, we figured out how to do it)
(b) The approximate change in revenue if production increases from 2.1 to 2.13 million units.
The change in revenue is about _____ thousand dollars.
(c) The approximate change in revenue if production decreases from 2.1 to 2.07 million units.
The change in revenue is about ______ thousand dollars.
(d) The approximate change in profit in parts (b) and (c).
The change in profit in part (b) is about ____ dollars, and the change in profit in part (c) is about ____ dollars.
If it helps, MC = C'(q), MR = R'(q), and profit = Total Revenue - Total Costs
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P = R - C
(a) P(2.1) = R(2.1) - C(2.1) = $6.9M - $5.2M = $1.7M (not $1.8M)
(b) ∆q = .03
∆R(2.1) = R(2.1 + .03) - R(2.1) ≈ ∆q*R'(2.1) = .03*$0.6M = $0.018M = $18k
(c) ∆q = -.03
∆R(2.1) ≈ ∆q*R'(2.1) = -.03*$0.6M = -$0.018M = -$18k
(d) ∆P = ∆R - ∆C ≈ ∆q*R' - ∆q*C' = ∆q*(R' - C')
R'(2.1) - C'(2.1) = $0.6M - $0.5M = $0.1M
(d):(b) ∆P(2.1) ≈ .03*$0.1M = $0.003M = $3k
(d):(c) ∆P(2.1) ≈ -.03*$0.1M = -$0.003M = -$3k
(a) P(2.1) = R(2.1) - C(2.1) = $6.9M - $5.2M = $1.7M (not $1.8M)
(b) ∆q = .03
∆R(2.1) = R(2.1 + .03) - R(2.1) ≈ ∆q*R'(2.1) = .03*$0.6M = $0.018M = $18k
(c) ∆q = -.03
∆R(2.1) ≈ ∆q*R'(2.1) = -.03*$0.6M = -$0.018M = -$18k
(d) ∆P = ∆R - ∆C ≈ ∆q*R' - ∆q*C' = ∆q*(R' - C')
R'(2.1) - C'(2.1) = $0.6M - $0.5M = $0.1M
(d):(b) ∆P(2.1) ≈ .03*$0.1M = $0.003M = $3k
(d):(c) ∆P(2.1) ≈ -.03*$0.1M = -$0.003M = -$3k