Aliyah is preparing to expand her IT consulting company. The current market rate for IT professionals is $58,000 per year. Each employee she hires will also require a computer and equipment that costs $6,000 per employee annually. Hiring more employees means that Aliyah can provide consulting services to more clients each year. Each client Aliyah has will pay her S10,000 per year. The number of clients Aliyah can take on is dependent on the number of workers she hires as shown in the accompanying table. What is the marginal cost and marginal benefit of hiring cach worker? Using the Rational Rule to maximize her economic surplus, how many workers should Aliyah hire?
Consider Ron’s demand for after school care for his children. The marginal benefit Ron receives for every hour of childcare is provided in the accompanying table. Using the Rational Rule for Buyers, if an hour of childcare costs $24. how many hours would Ron purchase each day? What about for S18 per hour? Draw Ron’s marginal benefit curve and his demand curve.
You own the only pharmacy in the small town of Jackson City, which has 40,000 residents. You would like to get a sense of what the local demand is for seasonal allergy medicine so you can determine how many packages to keep in stock and what price to charge. You conduct a survey of four residents of Jackson City, asking them about the quantity of allergy medicine they would buy each allergy season at various prices. Their responses are shown in the accompanying table. Estimate and graph the demand for the entire town of Jackson City.
The Correct Answer and Explanation is :
Aliyah’s IT Consulting Company: Marginal Cost and Marginal Benefit
To understand Aliyah’s decision-making process and the optimal number of employees to hire, we need to analyze both the marginal cost and marginal benefit.
Marginal Cost (MC)
The marginal cost is the additional cost incurred for hiring one more worker. This includes both the salary of the employee and the cost of the equipment. According to the problem:
- Salary of one employee: $58,000
- Cost of equipment per employee: $6,000
- Total marginal cost per employee = $58,000 (salary) + $6,000 (equipment) = $64,000
Therefore, the marginal cost of hiring each additional employee is $64,000.
Marginal Benefit (MB)
The marginal benefit refers to the additional revenue generated by hiring an additional worker. This depends on the number of clients that Aliyah can serve with each new hire.
- Each client pays $10,000 per year.
- The number of clients Aliyah can serve varies with the number of employees she hires (as per the provided table).
For example, if hiring 1 employee allows her to serve 5 clients, the additional revenue from hiring this employee would be:
- Revenue from 5 clients = 5 * $10,000 = $50,000
The marginal benefit for this worker would thus be $50,000.
Aliyah should compare the marginal cost with the marginal benefit to determine the optimal number of employees. According to the Rational Rule for maximizing economic surplus, hire workers until the marginal benefit equals or exceeds the marginal cost.
Ron’s Demand for After-School Care
We are given that the marginal benefit (MB) Ron receives for each hour of childcare is provided in the table, and we are also told the price per hour is $24.
Rational Rule for Buyers:
The Rational Rule for Buyers states that a buyer should continue purchasing a good until the marginal benefit is equal to or greater than the price. That is, Ron should continue purchasing childcare as long as the marginal benefit of each hour is greater than or equal to $24.
- If, for example, his marginal benefit for the first hour is $30, he will buy that hour of childcare.
- If his marginal benefit for the second hour drops to $18, he will not purchase that hour, since $18 is less than the price of $24.
Thus, based on this rule, if Ron’s marginal benefit is greater than or equal to $24, he will purchase that hour.
If the price drops to $18, Ron will purchase more hours, as his marginal benefit is higher than the price for more hours.
Jackson City’s Demand for Seasonal Allergy Medicine
To estimate the demand for allergy medicine in Jackson City, we will aggregate the responses of the four residents. Since Jackson City has 40,000 residents, we can project demand based on the survey.
Each resident in the survey reports how many packages of allergy medicine they would buy at various prices. By summing these responses for each price point and scaling them for the entire population, we can estimate the demand curve.
For example, if four residents report buying 1, 2, 3, and 4 packages at $10 each, then for the price of $10, the total demand from the survey is 10 packages. Multiply this by the population of Jackson City (i.e., 40,000 residents) to estimate the total demand.
Demand Curve:
Once the demand at each price point is estimated, the demand curve can be drawn by plotting these points. The demand curve will show the relationship between the price and the quantity demanded. As the price decreases, demand tends to increase, which forms a downward-sloping demand curve.
In summary, Aliyah should hire workers as long as the marginal benefit from additional employees is greater than the marginal cost of hiring them. Ron will purchase childcare hours as long as the marginal benefit exceeds the price. For the allergy medicine, the demand curve is constructed by aggregating survey responses and projecting for the town’s population.