P (price) 10 8 7 6 5 4 3 2 1 0
Q (output) 0 50 75 100 125 150 175 200 225 250
TR (Total Revenue) 0 400 525 600 625 600 525 400 225 0
MR (Marginal Revenue) - 8 5 3 1 -1 -3 -5 -7 -9
EP (Price Elasticity) ? ? ? ? ? ? ? ? ? ?
Complete the table, if demand function is Q = 250 – 25P .
Questions:
a. Describe the relationship between demand, TR, MR and price elasticity!
b. At what price the demand is inelastic, elastic, & unitary?
c. When demand is elastic and inelastic, should the price be lowered or should it be increased? Prove it with the numbers from the table.
a. The relationship between demand, total revenue (TR), marginal revenue (MR), and price elasticity can be described as follows:
- Demand: Demand represents the quantity of a good or service that consumers are willing and able to purchase at a given price. In this case, the demand function is Q = 250 - 25P, where Q is the quantity demanded and P is the price.
- Total Revenue (TR): Total revenue is the total amount of money earned from selling a given quantity of a good or service. It is calculated by multiplying the price (P) by the quantity demanded (Q). So, TR = P * Q.
- Marginal Revenue (MR): Marginal revenue is the additional revenue earned by selling one additional unit of a good or service. It is calculated as the change in total revenue divided by the change in quantity. In this case, since the demand function is linear, the marginal revenue can be found by observing the changes in total revenue for each change in quantity.
- Price Elasticity (EP): Price elasticity measures the responsiveness of quantity demanded to changes in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. It provides insight into how sensitive consumers are to price changes.
b. To determine the price at which demand is inelastic, elastic, or unitary, we need to consider the price elasticity of demand (EP).
- When demand is inelastic, EP is less than 1 (|EP| < 1).
- When demand is elastic, EP is greater than 1 (|EP| > 1).
- When demand is unitary, EP is equal to 1 (|EP| = 1).
To calculate price elasticity (EP), we can use the formula: EP = (ΔQ/Q) / (ΔP/P). By plugging in values from the table, we can calculate EP for each price level.
c. When demand is elastic, the absolute value of EP is greater than 1 (|EP| > 1). This means that consumers are highly responsive to price changes, and a small change in price will result in a relatively large change in quantity demanded. To maximize revenue in this case, the price should be lowered.
On the other hand, when demand is inelastic, the absolute value of EP is less than 1 (|EP| < 1). This indicates that consumers are not very responsive to price changes, and a change in price will have a relatively small impact on quantity demanded. To maximize revenue in this case, the price should be increased.
By analyzing the numbers in the table, we can determine the specific prices at which demand is inelastic, elastic, or unitary by identifying the corresponding EP values.