Question

If the monthly demand function is p = 8,500 - 6q2 and the supply function be taxation is p = 25+ 30q, what tax per item will maximize the total tax revenue Supply function after taxation = p= 25 + 3092 + t 25 + 3092 + t = 8500 - 697 2. For the following demand equation, p(q) = 10 - 0.22366 find the revenue equation, use calculus to find where the revenue is increasing and decreasing, sketch the graph of the revenue equation 3 For the following function, Display Settings ові ер 0 F4 F5 F6 F7 FB FO F10 F11 $ ( % 5 & 7 4 6 8 9 R. Y

Answer 1

Ans. Inverse demand function, p = 10 - 0.2236q^0.5

-400 gif (888.943, 2963.143) -3000 2000 -1000 (2000.122, 0) 0 1000 2000

=> Total revenue, TR = p*q = 10q - 0.2236q^1.5

=> Marginal revenue, MR = dTR/dq = 10 - 0.3354q^0.5

Total revenue is increasing if, MR > 0

=> 10 - 0.3354q^0.5 > 0

=> q < 888.943 units

Thus, total revenue is increasing when q < 888.943 units

Total revenue is decreasing if, MR < 0

=> q > 888.943 units

Thus, total revenue is decreasing when q > 888.943 units

And Total revenue is maximum where MR = 0,

Thus, 10 - 0.3354q^0.5 = 0

=> q = 888.943 units

So, total revenue is maximized at q = 888.943 units.

This means that the total revenue curve is an inverse U-shaped curve with maximum at q = 888.943 at which total revenue is $2963.143

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