I still don't understand how to calculate what the profit-maximizing tuition for full-time students? example when the cost for an additional unit is $125 and the part time students price elasticity is -2.5 and full time students is -1.8.
Im not sure I understand your question. In general, you want to set Marginal cost = Marginal revenue. You are given marginal cost. I don't think you can derive a marginal revenue from just a known demand elasticity. Further, its not clear from your question whether the school can price-discriminate -- that is, charge one price for full time, another for part time?
Do you have additional info you could provide?
Let me make a correction, we can approximate MR from an elasticity by the following formula MR=P*(1+1/e), where e is the elasticity.
So, we have, MC=125=MR=P*(1 - 1/1.8) for full timers. Solve for P. I get 281.25
Repeat for part-timers.
(I guess I would assume the school could price discriminate)
To calculate the profit-maximizing tuition for full-time students, you need to understand the concept of price elasticity of demand and its relationship to marginal revenue and marginal cost.
1. Determine the current tuition price for full-time students: Let's assume the current tuition price for full-time students is "X."
2. Calculate the demand elasticity for full-time students: The price elasticity of demand measures the responsiveness of quantity demanded to changes in price. In this case, the elasticity for full-time students is given as -1.8. This means that for every 1% increase in tuition price, the quantity demanded decreases by 1.8%.
3. Calculate the marginal revenue: Marginal revenue is the additional revenue generated by selling one additional unit. In this case, the cost for an additional unit is given as $125. Since marginal revenue is equal to the price in a competitive market, the marginal revenue for full-time students can be calculated as X + $125.
4. Determine the profit-maximizing tuition: The profit-maximizing tuition occurs where marginal revenue equals marginal cost. In this case, the cost for an additional unit is $125. Therefore, we need to set the marginal revenue (X + $125) equal to $125 to find the profit-maximizing tuition.
X + $125 = $125
Solving for X, we get,
X = $0
This means that the profit-maximizing tuition for full-time students is $0, indicating that full-time students would be willing to study for free.
However, it's important to note that this result seems unrealistic because the model assumes a linear relationship between price and quantity demanded, which might not hold in the real world. Additionally, other factors, such as costs, competition, and other market dynamics, should be considered when determining the actual tuition price.