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Orlov [11]
2 years ago
9

R. C. Barker makes purchasing decisions for his company. One product that he buys costs $50 per unit when the order quantity is

less than 500. When the quantity ordered is 500 or more, the price per unit drops to $48. The ordering cost is $30 per order and the annual demand is 7,500 units. The holding cost is 10 percent of the purchase cost. If R. C. orders 500 units each time he places an order, what would the total annual holding cost be
Business
1 answer:
aleksandrvk [35]2 years ago
6 0

Answer:

$1,200

Explanation:

total annual holding cost = average number of units in inventory x annual holding cost per unit

  • average number of units in inventory = 500 units / 2 = 250 units
  • annual holding cost per unit = $48 x 10% = $4.8

total annual holding cost = $4.80 x 250 units = $1,200

Total annual holding cost per unit includes all the costs associated to keeping a certain inventory level, e.g. warehouse costs like rent and utilities, salaries of hte employees that work in the warehouse, insurance, etc.

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Answer:

Equilibrium prices are p1 = 150 and p2 = 100, while equilibrium quantities are q1 = 150 and q2 = 5

Explanation:

To provide solution to this question, the two market demand functions to be restated correctly as follow:

q1 = D1(P1,P2) = 110 – p1 + 2p2 .................................... (1)

q2 = D2(p1,P2) = 55 – 2p2 + P1 ................................... (2)

Since, total revenue revue (TR) is the multiplication of price, p, and quantity, q, the TRs for q1 (TR1) and for q2 (TR2) are obtained by multiplying equation (1) by p1 and equation (2) by p2 as follows:

TR1 = p1*q1 = p1(110 – p1 + 2p2)

TR1 = p110 – p1^2 + 2p1p2 .................................... (3)

TR2 = p2*q2 = p2(55 – 2p2 + p1)

TR2 = p2(255) – 2p2^2 + p1p2 ................................... (4)

Marginal revenue for q1 (MR1) and for q2 (MR2) are obtained by partially differentiating equation (3) with respect to p1 and equation (2) with respect to p2 and then solve for p1 and p2 as follows:

MR1 = <em>d</em>TR1/<em>d</em>p1 = 110 – 2p1 + 2p2 .................................... (5)

MR2 = <em>d</em>TR2/<em>d</em>p2 = 55 – 4p2 + p1 ................................... (6)

In monopolistic competitive market with differentiated goods, equilibrium occurs where MR = MC. Since,

MC1 = 10 ..................................................................................... (7)

MC2 = 5 ...................................................................................... (8)

We will therefore equate equations (5) with equation (7) and also equate equation (6) with equation (8), and then solve for p1 and p2 as follows:

For MR1 = MC1:

110 – 2p1 + 2p2  = 10

2p1 = 110 - 10 + 2p2

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For MR2 = MC2:

255 – 4p2 + p1 = 5

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Now, substitute equation (10) for p2 in equation (9) and solve for p1 as follows:

p1 = 50 + 2(12.5 + p1/4)

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p1 = 75/0.5

p1 = 150 .......................................................................... (11)

substitute equation (11) into equation (10) for p1 and solve for p2 as follows, we have:

p2 = 62.5 + 150/4

p2 = 62.5 + 37.5

p2 = 100 ............................................................... (12)

The p1 and p2 in equations (11) and (12) are the equilibrium prices for q1 and q2 respectively.

To get equilibrium quantity, substitute p1 = 150 and p2 = 100 into equations (1) and (2) as follows:

q1 = 110 – 150 + 2(100)

q1 = – 50 + 200

q1 = 150  .................................... (13)

q2 = 55 – 2(100) + 150

q2 = 55 + 150 - 200

q2 = 5  ....................................... (5)

Therefore, equilibrium prices are p1 = 150 and p2 = 100, while equilibrium quantities are q1 = 150 and q2 = 5.

3 0
2 years ago
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