Many Software Companies After Years Of Providing Unlimited F
Many Software Companies After Years Of Providing Unlimited Free Telep
Many software companies, after years of providing unlimited free telephone technical support for their products, began to charge for these services (typically after an initial start-up period of 90 days). Most companies offer two pricing plans. Suppose, for instance, Lotus Development offers users of their spreadsheet software the option of paying either (i) $2.00 per minute for telephone support or (ii) a $129 flat charge for a year of unlimited toll-free calls. Consider a customer with a yearly demand for service support of P = 11 – 0.1Q, where P is the price per minute and Q is the number of minutes of calls made per year. How many minutes of calls would this customer make under plan (i)? How many minutes of calls would he or she make under plan (ii)? Calculate the consumer surplus for each of the plans (i) and (ii).
Paper For Above instruction
This paper analyzes the customer behavior and consumer surplus for two different support pricing plans offered by Lotus Development: a pay-per-minute plan and a flat-rate plan. The analysis revolves around the customer’s demand function and the economic implications of each pricing strategy, ultimately determining usage levels and consumer surplus under each scenario.
Customer Demand Function and Pricing Plans
The demand for telephone support service by a customer is given by the linear demand equation P = 11 – 0.1Q, where P is the price per minute and Q is the number of minutes per year. This demand curve indicates that as the price per minute declines, the quantity of minutes demanded increases. The customer’s willingness to pay diminishes with increasing usage, reflecting typical consumer behavior in response to price changes.
Lotus Development’s two plans are as follows:
1. Plan (i): Pay $2.00 per minute of support.
2. Plan (ii): Pay a flat fee of $129 for unlimited calls.
Calculating Minutes of Calls under Plan (i):
Under the pay-per-minute plan, the quantity of minutes Q can be determined by equating the price per minute from the demand function to the plan’s rate.
Given:
\[ P = 11 - 0.1Q \]
Set:
\[ P = 2.00 \]
Solve for Q:
\[
2.00 = 11 - 0.1Q
\]
\[
0.1Q = 11 - 2.00
\]
\[
0.1Q = 9
\]
\[
Q = \frac{9}{0.1} = 90
\]
Thus, the customer would make 90 minutes of calls annually under the pay-per-minute plan.
Calculating Minutes of Calls under Plan (ii):
Under the flat-rate plan, there is effectively no marginal cost per minute beyond the fixed fee, assuming the customer’s willingness to pay exceeds or equals $129.
- The maximum willingness to pay per minute occurs at Q = 0:
\[
P = 11 - 0.1 (0) = 11
\]
which is greater than the flat rate of $129, indicating the customer would use as many minutes as they desire since the marginal cost per minute ($2) is less than their willingness to pay at zero usage.
- To determine the maximum quantity of minutes the customer would consume at the flat rate, find the price at the point where the customer’s willingness to pay drops to $129 per year. However, since per-minute prices are not directly multiplied by Q for the flat rate, the flat-rate plan covers the entire demand curve up to the point where the total consumer surplus is maximized, i.e., the point where the total value of support equals the fixed fee.
Alternatively, because the customer’s demand decreases with increasing P, and the flat fee is fixed, the customer will purchase support up to the point where their willingness to pay per minute is at or above the equivalent marginal benefit.
But more straightforwardly, given the customer’s demand curve:
\[
Q = \frac{11 - P}{0.1}
\]
At P approaching zero (theoretically), the demand would be:
\[
Q_{max} = \frac{11 - 0}{0.1} = 110
\]
and at the maximum willingness to pay per minute (which is $11 at Q=0), and the flat fee of $129:
Since the flat fee is a fixed cost, and the total willingness to pay (total consumer surplus plus total cost) is:
\[ \text{Total Willingness to Pay} = \int_{0}^{Q} P \, dQ \]
The consumer will use:
\[
Q_{flat} = \text{the demand at P = 0} = 110 \text{ minutes}
\]
because the price per minute is effectively zero for the consumer at the flat rate; the total value exceeds the flat fee, making usage maximal.
Consumer Surplus Calculation
1. Under Plan (i):
The consumer’s surplus is the area between the demand curve and the price paid, up to the quantity Q = 90 minutes.
- The demand curve intercepts the price axis at P = 11 (when Q=0).
- The consumer spends:
\[ \text{Expenditure} = P \times Q = 2 \times 90 = \$180 \]
- The total value of support consumers derive is the area under the demand curve:
\[
\text{Total Willingness to Pay} = \int_0^{90} (11 - 0.1Q) dQ
\]
\[
= \left[11Q - 0.05Q^2 \right]_0^{90}
\]
\[
= 11 \times 90 - 0.05 \times 90^2
\]
\[
= 990 - 0.05 \times 8100
\]
\[
= 990 - 405 = 585
\]
- Consumer surplus (CS) is:
\[
CS = \text{Total Willingness to Pay} - \text{Expenditure}
\]
\[
CS_{plan\ (i)} = 585 - 180 = \$405
\]
2. Under Plan (ii):
At the flat rate of $129, the customer optimally consumes 110 minutes, as shown earlier.
- Total value of support at 110 minutes:
\[
\text{Total Willingness to Pay} = \int_0^{110} (11 - 0.1Q) dQ
\]
\[
= 11 \times 110 - 0.05 \times 110^2
\]
\[
= 1210 - 0.05 \times 12100
\]
\[
= 1210 - 605 = \$605
\]
- Consumer surplus is total willingness to pay minus the flat fee:
\[
CS_{plan\ (ii)} = 605 - 129 = \$476
\]
Implications and Analysis
The above calculations reveal that, under the pay-per-minute plan, the customer would use 90 minutes and attain a consumer surplus of $405. Conversely, the flat-rate plan encourages higher usage (up to 110 minutes) and provides a higher consumer surplus of $476, implying better value for the customer. This supports common economic theory—the flat-rate reduces marginal costs to zero, incentivizing higher consumption and increasing consumer welfare, assuming the demand curve remains valid over the expanded usage.
Additionally, the consumer surplus difference illustrates the incentive for the customer to prefer the flat-rate plan, as it offers higher welfare. However, the service provider must consider their profit margins, as higher usage under flat-rate plans might incur higher costs.
Conclusion
This analysis highlights key aspects of pricing strategy and consumer behavior in support services. The customer would use approximately 90 minutes under the pay-per-minute plan with a consumer surplus of $405; under the flat-rate plan, maximum usage is 110 minutes, yielding a consumer surplus of $476. The choice between plans depends on the customer’s expected usage and their valuation of support, providing valuable insights for companies designing such pricing models.
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