Math Problem Statement

The following graph displays four supply curves (LL, MM, NN, and OO) that intersect at point V. A graph with price in dollars per unit on the y-axis and quantity of units on the x-axis plots 4 line segments, L L from (6, 4) to (14, 16), M M from (3, 10) to (17, 10), N N from (10, 3) to (10, 17), and O O from (4, 6) to (16, 14). The graph also plots five points: V (10, 10) is the intersection of all four line segments. W (10, 13) is on line segment N N. X (12, 13) is on line segment L L. Y (13, 12) is on line segment O O. Z (13, 10) is on line segment M M. 0 2 4 6 8 10 12 14 16 18 20 20 18 16 14 12 10 8 6 4 2 0 PRICE (Dollars per unit) QUANTITY (Units) V W X Y Z M M O O L L N N Using the graph, complete the table that follows by indicating whether each statement is true or false. Statement True False Curve OO is less elastic between points V and Y than curve LL is between points V and X.

Between points V and W, curve NN is perfectly inelastic.

Between points V and Y, curve OO is inelastic.

Solution

Let's analyze the statements one by one based on the information provided in the graph and supply curves.

1. "Curve OO is less elastic between points V and Y than curve LL is between points V and X."

  • Elasticity is the responsiveness of the quantity supplied to a change in price. More elastic curves respond more to changes in price, while less elastic (or inelastic) curves respond less.

  • Curve OO (from V to Y): From point V(10,10)V(10, 10) to Y(13,12)Y(13, 12), there is a small change in both quantity (3 units) and price (2 dollars). Since both quantity and price change only slightly, this suggests a more inelastic behavior (lower elasticity).

  • Curve LL (from V to X): From point V(10,10)V(10, 10) to X(12,13)X(12, 13), there is a change of 2 units in quantity and 3 dollars in price. There is a slightly larger price change for a smaller quantity change, suggesting that curve LL is more elastic than curve OO between these points.

So, Curve OO is less elastic than curve LL between these points, which makes this statement True.

2. "Between points V and W, curve NN is perfectly inelastic."

  • Perfect inelasticity occurs when the quantity does not change regardless of the change in price, meaning the curve is vertical.

  • Curve NN is a vertical line through point V(10,10)V(10, 10) and W(10,13)W(10, 13), indicating that the quantity is fixed at 10 units regardless of the price. This is the definition of perfect inelasticity.

Therefore, this statement is True.

3. "Between points V and Y, curve OO is inelastic."

  • Inelasticity means that the percentage change in quantity supplied is less than the percentage change in price.

  • From point V(10,10)V(10, 10) to point Y(13,12)Y(13, 12) on curve OO, the quantity increases by 3 units, while the price increases by 2 dollars. Since the quantity change is larger than the price change, this suggests a relatively elastic response (more sensitive to changes in quantity than price).

Hence, this statement is False.

Summary of True/False:

StatementTrue/False
Curve OO is less elastic between points V and Y than curve LL is between points V and X.True
Between points V and W, curve NN is perfectly inelastic.True
Between points V and Y, curve OO is inelastic.False

Would you like further details or clarification on any of these points?

Here are five questions you can explore further:

  1. How is elasticity calculated for linear supply curves?
  2. Why is curve NN perfectly inelastic, and how does this impact market behavior?
  3. How do changes in price affect elastic vs. inelastic supply curves in the long run?
  4. What factors determine the elasticity of a supply curve?
  5. How can elasticity influence government tax policies on goods?

Tip: Elasticity can vary at different points along the same supply curve—understanding how to calculate it using the formula can be insightful.

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Math Problem Analysis

Mathematical Concepts

Supply Curves
Elasticity
Inelasticity

Formulas

Elasticity = (Percentage change in quantity) / (Percentage change in price)

Theorems

Law of Supply
Perfect Inelasticity

Suitable Grade Level

Grades 11-12 (Advanced Economics)