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Sagot :
Answer:
The answer is "2,400, 3,600, and 2,400".
Explanation:
Please find the complete question in the attached file.
using the table to calculate the linear demand function.
Function Linear Demand:[tex]P = a - bQ[/tex]
[tex]Q = 2,000\\\\P = 2 \\\\Q = 400\\\\P = 10[/tex]
[tex]2 = a - 2,000b.........(1)\\\\10 = a - 400b..........(2) \\\\\ subtract \ equation \ (2) \ from \ (1):\\\\1,600b = 8\\\\b=\frac{8}{1600}\\\\ b = 0.005\\\\ a = 10 + 400b [From \ equation \ (2)] = 10 + 400 x 0.005 = 10 + 2 = 12\\\\Demand \ function( P) = 12 - 0.005Q[/tex]
In point (i)
[tex]P = 6\\\\6 = 12 - 0.005Q\\\\ 0.005Q = 6\\\\Q = 1200\\\\\to Net\ benefit\ = Q \times (P - MC) \\\\[/tex]
[tex]= 1200 \times (6 - 4)\\\\ = 1200 \times 2\\\\ = \$2,400[/tex]
In point (ii)
If Q = 0, P = 12 (vertical intercept of demand curve)
Cost surplus = surface area
[tex]=(\frac{1}{2}) \times (12 - 6) \times 1200 \\\\ = 600 \times 6 \\\\ =\$3,600[/tex]
In point (iii)
Surplus for producer = region of MC curve and price
[tex]= (6 - 4) \times 1200 \\\\ = 1200 \times 2 \\\\= \$2,400[/tex]
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