Only need help with 6 7 and 8 This has to be written in the

** Only need help with 6, 7, and 8.  This has to be written in the form of a paper so any extra insight on how the calculations were made and what they mean 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?

Solution

Q = 2000 - 20P

20P = 2000 - Q

P = 100 - 0.05Q

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

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

(6) When P = $60, Q = 2000 - (20 x 60) = 2000 - 1200 = 800

TR = P x Q = $60 x 800 = $4800

MR = 100 - (0.1 x 800) = 100 - 80 = $20

Elasticity = (dQ/dP) x (P/Q) = - 20 x (60/800) = - 1.5

(7) Elasticity is unitary when [(dQ/dP) x (P/Q)] = - 1

-20 x [P / (2000 - 20P)] = - 1

20P / (2000 - 20P) = 1

20P = 2000 - 20P

40P = 2000

P = $50

(8) The demand curve for product X is downward sloping. Therefore product X follows the law of demand, so that when price increases (decreases), quantity demanded decreases (increases). Since it is not a Giffen good, it is expected that when consumer income decreases, consumers will decrease their demand for product X.