Problem 1: Using the Marginal Cost Approach
The marginal cost is the change in total cost as a result of the change of producing one additional product. The shuttle business has different customer loads with varying cost. The marginal cost of the Shuttle business can be determined by the following formula.
The marginal cost = the change in total cost /Change in the output level. It is the change in total costs as a result of increase in the quantity produced by one unit . The calculated marginal cost is as shown in the table below.
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| Output (customers) | Cost ($) | Marginal Cost ($) |
| 1 | 30 | |
| 2 | 32 | 2 |
| 3 | 35 | 3 |
| 4 | 38 | 3 |
| 5 | 42 | 4 |
| 6 | 48 | 6 |
| 7 | 57 | 9 |
| 8 | 68 | 11 |
If compensated $ 10 dollar per ride. It is important to identify the production level where marginal costs are equal to marginal revenue. It is at the point where marginal cost equals marginal revenue that profit is maximized. From the calculation, it is evident that the marginal cost of the company is increasing as the organization increasing its production level. At the point where the vehicle carries 7 people where marginal l cost is 9. Carrying more than that will result in higher marginal cost than the proposed marginal revenue of 10. It is thus at customer load of 7 passengers where profit is maximized.
Problem 2: Elasticity and Pricing
The price elasticity of demand measures the change in the quantity demanded as a result of the changes in prices. It is always negative since the demand curve is always leftward sloping. As the level of competition in a business environment increases, there is likelihood for a change in price elasticity. The company demand elasticity increased from -2 to -3 due to increase in the level of competition.
In this case, it is important to determine the link between the marginal revenue and price elasticity. When the marginal revenue of a company is positive, the total revenue increases and this means that the demand is elastic. On the other hand, the negative marginal revenue means that the total revenues are decreasing with an increase in quantity demanded while the demand is price inelastic.
The optimal price is normally the output level where the marginal revenue is equal to the marginal costs. The relationship between the marginal revenue, price and price elasticity is as shown in the formula below.
Price elasticity of demand percentage change in quantity/percentage change in price
MR = P (1 + (1/E)
The MC = MR at the optimal output level, thus
MC= P (1 + (1/E)
P = MC/ (1-(1/E)
(P-MC)/P = 1/E
Given a price level of $ 10and the elasticity of -2, the marginal cost is determined as (10-MC)/10 = ½
10-MC = 10/2
10-MC= 5
MC = 10-5 = 5
Assuming the new price is p1, the following equation applies.
(P1-5)/P1 = ½
P1 – 5 = 0.5P
P1 = 5
Thus, the company should charge $ 5 to comply with the new market condition.
Problem 3: Price Discrimination
|
Price ($) |
Quantity |
|
|
Adults |
Children |
|
|
5 |
15 |
20 |
|
6 |
14 |
18 |
|
7 |
13 |
16 |
|
8 |
12 |
14 |
|
9 |
11 |
12 |
|
10 |
10 |
10 |
|
11 |
9 |
8 |
|
12 |
8 |
6 |
|
13 |
7 |
4 |
|
14 |
6 |
2 |
For adult market, the calculated total revenue (TR), marginal revenue (MR), total cost (TC) and profit (P) is shown in the table below.
| Price ($) | Quantity | ||||
| Adults | TR | MR | TC | Profit | |
|
5 |
15 |
75 |
75 |
0 |
|
|
6 |
14 |
84 |
-9 |
70 |
14 |
|
7 |
13 |
91 |
-7 |
65 |
26 |
|
8 |
12 |
96 |
-5 |
60 |
36 |
|
9 |
11 |
99 |
-3 |
55 |
44 |
|
10 |
10 |
100 |
-1 |
50 |
50 |
|
11 |
9 |
99 |
1 |
45 |
54 |
|
12 |
8 |
96 |
3 |
40 |
56 |
|
13 |
7 |
91 |
5 |
35 |
56 |
|
14 |
6 |
84 |
7 |
30 |
54 |
The adult market profit is $ 56, the price is $ 12, and quantity is 8. In essence, the company maximizes its profit at this level since it is the point at which the company earns the highest profit.
The calculation of the profit, total revenue (TR), marginal cost (MC) and total cost (TC) are as shown in the table below.
| Price ($) | Children | TR | MR | TC | Profit |
|
5 |
20 |
100 |
100 |
0 |
|
|
6 |
18 |
108 |
-8 |
90 |
18 |
|
7 |
16 |
112 |
-4 |
80 |
32 |
|
8 |
14 |
112 |
0 |
70 |
42 |
|
9 |
12 |
108 |
4 |
60 |
48 |
|
10 |
10 |
100 |
8 |
50 |
50 |
|
11 |
8 |
88 |
12 |
40 |
48 |
|
12 |
6 |
72 |
16 |
30 |
42 |
|
13 |
4 |
52 |
20 |
20 |
32 |
|
14 |
2 |
28 |
24 |
10 |
18 |
For the children the profit is $ 50, quantity is 10 and the price is $ 10. This is the point that the company can maximize its profits. The maximum profit for adults is $56 at $12 per person for 8 adults and the maximum profit for children is $50 at $10 per person for 10 children .
For the combined markets, it is important to add the profits of the two firms and determine the points where it is able to earn the high profits. The calculation for the combine market is shown in the table below.
| Adult | Adult | Children | Children | Combined Profit | |
| Price ($) | Quantity | Profit | Quantity | Profit | |
|
5 |
15 |
0 |
20 |
0 |
0 |
|
6 |
14 |
14 |
18 |
18 |
32 |
|
7 |
13 |
26 |
16 |
32 |
58 |
|
8 |
12 |
36 |
14 |
42 |
78 |
|
9 |
11 |
44 |
12 |
48 |
92 |
|
10 |
10 |
50 |
10 |
50 |
100 |
|
11 |
9 |
54 |
8 |
48 |
102 |
|
12 |
8 |
56 |
6 |
42 |
98 |
|
13 |
7 |
56 |
4 |
32 |
88 |
|
14 |
6 |
54 |
2 |
18 |
72 |
When the same price is charged in both markets combined, it is evident that total revenues decline. Children have lower purchase capability as compared to women.
Problem 4: Bundling
If the d Showtime and History Channel are sold separately, Customer 1 would pay $9 for Showtime and Customer 2 would pay $8 for History Channel for $17. Less the licensing fees of $1 each, the organization would make $15 profit from selling separately. On the other hand, both customers are willing to buy as a bundle at $11 for both channels (bundling). Then each customer would pay $11, giving a total combined $22 for both less $2 for licensing fees for each, resulting in $18 in profit. Bundling of the channels would thus be better. In the second option , both customers would be willing to pay $11 for both channels (bundling). Then each customer would pay $11 less $2 for licensing fees, giving you $18 in profit. Bundling is better .
If everyone likes Showtime more than History channel, the Time Warner should not bundle. This is because, it should leverage on the number of the customers from Showtime to ensure that it generates high revenue. In the vent that Time Warner sells Show Time for $ 9 and History channel at $ 8, it should consider selling in bundles since both are able to earn high total revenues of $ 11 each before $1 costs each.
In mixed bundling, there is a bundle charge $8 for Showtime and $5 for History Channel. This would result in $13 bundle. Then Customer 1 would pay $9 for Showtime, Customer 2 would pay $8 for History Channel and someone else could pay $13 for both, less $4 for licensing fees for a $26 profit. Mixed bundling should thus be adopted
