Any additional information on how the answers were calculated is appreciated. Th

Question

Any additional information on how the answers were calculated is appreciated.

The demand curve for product X is given as Q= 2000-20P 1. How many units will be sold at $10 2. At what price would 2,000 units be sold? 0 units? 1,500 units? 3. Write equations for total revenue and marginal revenue (in terms of Q) 4. What will be the total revenue at a price of $70? What will be the marginal revenue? 5. What is the point elasticity at a price of $70? 6. If price were to decrease to $60, what would total revenue, marginal revenue and point elasticity be now? 7. At what price would elasticity be unitary? 8. In your opinion, should consumers change their demand when their income decreases?

Explanation / Answer

Q = 2000 - 20P

(1) When P = $10, Q = 2000 - (20 x 10) = 2000 - 200 = 1800

(2) Q = 2000 - 20P, or 20P = 2000 - Q, or P = 100 - 0.05Q

(i) When Q = 2,000, P = 100 - (0.05 x 2000) = 100 - 100 = 0

(ii) When Q = 0, P = 100 - (0.05 x 0) = 100 - 0 = $100

(iii) When Q = 1500, P = 100 - (0.05 x 1500) = 100 - 75 = $25

(3)

Total revenue (TR) = P x Q = 100Q - 0.05Q2

Marginal revenue (MR) = dTR/dQ = 100 - 0.1Q

(4) When P = $70, Q = 2000 - (20 x 70) = 2000 - 1400 = 600

TR = P x Q = $70 x 600 = $42000

MR = 100 - (0.1 x 600) = 100 - 60 = $40

(5) When P = $70, Q = 2000 - (20 x 70) = 2000 - 1400 = 600

Point elasticity = (dQ/dP) x (P/Q) = - 20 x (70/600) = - 2.33

NOTE: As per Chegg Answering Policy, first 5 questions are answered.

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