Final answer:
The change in producer surplus resulting from a price increase from $50 to $60 is calculated using the supply equation P = 30 + 0.25Q. The quantities supplied at the initial and final prices are found to be Q0 = 80 and Q1 = 120 units respectively, leading to a change in producer surplus of $200.
Step-by-step explanation:
Producer surplus is a measure of producer welfare. It is the amount received from selling a product minus the minimum amount that the producer would be willing to accept for providing the product. The market supply equation given is P = 30 + 0.25Q, where P is the price and Q is the quantity.
The change in producer surplus can be found as the area of the triangle that lies under the supply curve and above the initial and final prices. When the price increases, the producer surplus increases as well. Initially, the market price increases from P0 = $50 to P1 = $60, indicating an increase in producer surplus.
To calculate the change in producer surplus, we identify the quantities supplied at both prices Q0 and Q1 using the supply equation. Then, we calculate the area of a right triangle with height equal to the price change (P1 - P0) and base equal to the change in quantity (Q1 - Q0).
- First, find Q0 and Q1 by substituting P0 and P1 into the supply equation:
- 50 = 30 + 0.25Q0 => Q0 = 80
- 60 = 30 + 0.25Q1 => Q1 = 120
Calculate the change in quantity: Q1 - Q0 = 120 - 80 = 40.Calculate the change in price: P1 - P0 = 60 - 50 = 10.Now calculate the area of the triangle, which is the change in producer surplus: (1/2) * change in price * change in quantity = (1/2) * 10 * 40 = $200.
Therefore, the change in producer surplus due to the price increase is $200.