A friend of yours is considering two cell phone service...

A friend of yours is considering two cell phone service providers. Provider A charges $\$ 120$ per month for the service regardless of the number of phone calls made. Provider B does not have a fixed service fee but instead charges $\$ 1$ per minute for calls. Your friend's monthly demand for minutes of calling is given by the equation $Q^{\mathrm{D}}=150-50 P,$ where $P$ is the price per minute. a. With each provider, what is the cost to your friend of an extra minute on the phone? b. In light of your answer to (a), how many minutes with each provider would your friend talk on the phone? c. How much would she end up paying each provider every month? d. How much consumer surplus would she obtain with each provider? (Hint: Graph the demand curve and recall the formula for the area of a triangle. e. Which provider would you recommend that your friend choose? Why?

A friend of yours is considering two cell phone service providers. Provider A charges $\$ 120$ per month for the service regardless of the number of phone calls made. Provider B does not have a fixed service fee but instead charges $\$ 1$ per minute for calls. Your friend's monthly demand for minutes of calling is given by the equation $Q^{\mathrm{D}}=150-50 P,$ where $P$ is the price per minute.
a. With each provider, what is the cost to your friend of an extra minute on the phone?
b. In light of your answer to (a), how many minutes with each provider would your friend talk on the phone?
c. How much would she end up paying each provider every month?
d. How much consumer surplus would she obtain with each provider? (Hint: Graph the demand curve and recall the formula for the area of a triangle.
e. Which provider would you recommend that your friend choose? Why?

Key Concepts

Demand Function

A demand function expresses the relationship between the price of a good or service and the quantity demanded by consumers. It demonstrates how changes in price affect consumer behavior and is foundational in understanding how different pricing strategies can influence consumption. In this context, the demand curve is used to determine how many minutes of calls the friend will use at different per?minute prices.

Marginal Cost

Marginal cost refers to the additional cost incurred when one more unit of a good or service is consumed. It is critical in decision-making because it helps determine the optimal level of consumption by comparing the cost of an extra unit to the benefit or willingness to pay for that unit. Here, it is used to analyze the cost of an extra minute of phone usage under differing pricing structures.

Fixed Fee versus Variable Pricing

Fixed fee versus variable pricing contrasts a pricing strategy where a flat fee is charged regardless of usage with one where costs vary directly with the quantity consumed. Fixed fee pricing (or a flat-rate model) often leads to a marginal cost of zero for additional consumption, encouraging higher usage, while variable pricing means consumers pay an extra amount for each additional unit. This concept is essential for evaluating how the structure of fees influences overall consumption decisions.

Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good or service (as indicated by the demand curve) and what they actually pay. It is represented graphically as the area between the demand curve and the price level up to the quantity consumed. This concept is key to understanding the net benefit to consumers from different pricing schemes, as it captures the extra value or utility derived from consumption beyond the cost incurred.

Optimal Consumption Decision

An optimal consumption decision involves choosing the level of consumption that maximizes a consumer’s net benefit or utility, given the trade-off between the cost of additional units (marginal cost) and the willingness to pay (demand curve). In scenarios with different pricing models, consumers compare their marginal benefit with the marginal cost under each model to decide how much to use, ensuring that every additional unit provides a benefit equal to or exceeding its cost.

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