Willy's widgets, a monopoly, faces the following demand schedule (sales of widgets per month):
Price $20 30 40 50 60 70 80 90 100
Quantity 40 35 30 25 20 15 10 5 0
Calculate marginal revenue over each interval in the schedule (for example, between Q = 40 and Q=35). Recall that the revenue is the added revenue from an additional unit of production/sales and assume MR is constant within each interval.
If marginal cost is constant at $20 and total fixed cost is $100, what is the profit maximizing output level and price. Does the firm earn a profit or loss and how much is it?
Here's what I got...although I would double-check my work as I quickly input the data. After running a regression analysis, I got an inverse demand function of P = 100 - 2Q. MR = a + 2bQ and MC = 20. Therefore, equating MR and MC will provide the profit-maximizing quantity. Once the quantity is derived, input that number in the inverse demand function to get your profit-maiximizing price. The rest is down hill. Calculate total revenue, then subtract total costs from this to get profit. Again, double-check my work.
1) In using regression analysis for making predictions what are the assumptions
involved.
2 What is a simple linear regression model?
3) What is a scatter diagram method?
To calculate the marginal revenue over each interval, first, you need to find the change in total revenue for each change in quantity. Marginal revenue is the additional revenue generated from selling one more unit.
Looking at the demand schedule, you can see that the quantity decreases by 5 for each price increase of $10.
For Q = 40 to Q = 35:
The change in quantity is 5 units, and the corresponding change in revenue is ($30 - $20) * 5 = $50. So the marginal revenue in this interval is $50.
Similarly, for the remaining intervals:
Q = 35 to Q = 30: Marginal revenue = ($40 - $30) * 5 = $50
Q = 30 to Q = 25: Marginal revenue = ($50 - $40) * 5 = $50
Q = 25 to Q = 20: Marginal revenue = ($60 - $50) * 5 = $50
Q = 20 to Q = 15: Marginal revenue = ($70 - $60) * 5 = $50
Q = 15 to Q = 10: Marginal revenue = ($80 - $70) * 5 = $50
Q = 10 to Q = 5: Marginal revenue = ($90 - $80) * 5 = $50
Q = 5 to Q = 0: Marginal revenue = ($100 - $90) * 5 = $50
Now, let's move on to finding the profit-maximizing output level and price.
To determine the profit-maximizing quantity, equate marginal revenue (MR) to marginal cost (MC). In this case, MR = $50 and MC = $20.
So, $50 = $20 + 2bQ (where Q represents the quantity)
Solving this equation, we get 2bQ = $30, and since MC = $20, Q = 15.
Now, plug the value of Q into the inverse demand function to find the profit-maximizing price:
P = 100 - 2Q
P = 100 - 2 * 15
P = 70
Therefore, the profit-maximizing output level is 15 units, and the price is $70.
To calculate the profit, we need to compute the total revenue (TR) and total cost (TC).
Total Revenue:
TR = Quantity * Price
TR = 15 * $70
TR = $1050
Total Cost:
TC = Total Fixed Cost + (Variable Cost per unit * Quantity)
TC = $100 + ($20 * 15)
TC = $400
Profit:
Profit = TR - TC
Profit = $1050 - $400
Profit = $650
Therefore, the firm earns a profit of $650.