Production Cost Per Edition Is Tc (Q) Essay

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Production Cost Per Edition Is

TC (Q) =70+0.10Q+0.001Q2

Functions

(i) Total Revenue Function

Total Revenue is normally calculated by multiplying the price of the product with the quantity sold.

TR (Q) =P (Q) x Q. where Q. is the quantity of output sold, and P (Q) is the inverse demand function of the price.

Price per unit is

Simplified function 0.90Q2

Profit Function

The profit is calculated by subtracting the production cost from the total revenue

(Q) = TR (Q) - TC (Q)

Production cost =70+0.10Q+0.001Q2

P (Q) x Q -- (70+0.10Q+0.001Q2) where P. Or ? is the price per Unit

PQ2-70+0.10Q+0.001Q2

Price per copy is

Q2 -70+0.10Q+0.001Q2

Profit Function = 0.9010 Q2 +0.10Q -70

Marginal Revenue Function

The marginal revenue is the extra revenue that comes from selling 1 additional unit. The change in revenue with respect to a change in quantity must be computed first.

MR (Q)= d (TR) Where'd represent derivative dQ

Total Revenue function = 0.90Q2

MR (Q)= d (TR) =d (0.90Q2)

dQ d (Q)

Marginal cost Function

The marginal unit is the last unit. Therefore, marginal cost is the cost of the last unit, or what it costs to produce one more unit. The change in costs from a previous level divided by the change in quantity from the previous level is represented by MC = Change in TC / Change in Q

MC (Q)= d (TC)

d (Q)

The function is =MC (Q)=d (70+0.

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10Q+0.001Q2)

d (Q)

Marginal profit Function

M ? = R ' (Q) - C ' (Q)

Marginal revenue is d (0.90Q2) - d (70+0.10Q+0.001Q2)

d (Q) d (Q)

M ? = 0.90Q2 - (70+0.10Q+0.001Q2 )

QQ

M ? = 0.90Q - (70+0.10Q+0.001Q2 )

Q

Average cost function

Average cost is total revenue divided by the number of quantity

MC= 0.90Q2

Q

Manipulate the total revenue, profit, marginal revenue, marginal cost, marginal profit and average cost given that Q=500

Total revenue

TR (Q) =P (Q) x Q= 0.90Q2

0.90 x 5002 =0.90 x 250000

TR=225000

(i) Profit

Profit function is 0.9010 Q2 +0.10Q -70

Q=500

(0.9010 x 5002 ) + (0.10 x 500) -- 70

225250 + 50-70

P =225230

(ii) Marginal Revenue

Marginal revenue function is MR (Q) = d (TR) =d (0.90Q2)

dQ d (Q)

Q=500

=d (0.90Q2)

d (Q)

500 = 0.90 x 250000 = 450

MR = 450

(iii) Marginal cost

The MC function is d (70+0.10Q+0.001Q2)

d (Q)

Q=500

d (70+0.10Q+0.001Q2)

d (Q) = 70+0.10Q+0.001Q2

Q

70+ (0.10 x 500) + (0.001 x 5002 ) = 70+50 +250

MC = 370

(iv) Marginal profit

The marginal profit function is

M ? = 0.90Q - (70+0.10Q+0.001Q2)

Q

Q= 500.....

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