Suppose the supply for a certain textbook is given by p= 2 29 and demand is given by p= -29+30, where p is the price and q is the quantity. (a) How many books are demanded at a price of $20? (b) How many books are supplied at a price of $20? (c) Graph the supply and demand functions on the same axes. (a) How can the number of books demanded be found? OA. Substitute the price for q in the demand equation. B. Substitute the price for p in the demand equation. OC. Solve each equation for q and set the resulting expressions equal to each other. OD. Set the two expressions for p equal to each other. The number of books that are demanded at a price of $20 is (Round to the nearest whole number as needed)

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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**Supply and Demand Analysis for a Textbook**

Suppose the supply for a certain textbook is given by the equation \( p = \frac{1}{2} q^2 \) and demand is given by \( p = -\frac{1}{2} q^2 + 30 \), where \( p \) is the price and \( q \) is the quantity.

**Tasks:**
1. **Determine the Number of Books Demanded at a Price of $20:**
   - **Option A:** Substitute the price for \( q \) in the demand equation.
   - **Option B:** Correct. Substitute the price for \( p \) in the demand equation.
   - **Option C:** Solve each equation for \( q \) and set the resulting expressions equal to each other.
   - **Option D:** Set the two expressions for \( p \) equal to each other.

   The number of books that are demanded at a price of $20 is \( \_\_\_\_\_\_\_ \). (Round to the nearest whole number as needed.)

2. **Determine the Number of Books Supplied at a Price of $20.**

3. **Graph the Supply and Demand Functions on the Same Axes.** 

**Graph Explanation:**
- The graph comprises two curves representing supply and demand against quantity and price axes.
- The supply curve \( p = \frac{1}{2} q^2 \) is upward sloping, indicating that higher prices encourage more supply.
- The demand curve \( p = -\frac{1}{2} q^2 + 30 \) is downward sloping, suggesting that lower prices encourage higher demand.
- The intersection point of the two curves represents the equilibrium price and quantity.
Transcribed Image Text:**Supply and Demand Analysis for a Textbook** Suppose the supply for a certain textbook is given by the equation \( p = \frac{1}{2} q^2 \) and demand is given by \( p = -\frac{1}{2} q^2 + 30 \), where \( p \) is the price and \( q \) is the quantity. **Tasks:** 1. **Determine the Number of Books Demanded at a Price of $20:** - **Option A:** Substitute the price for \( q \) in the demand equation. - **Option B:** Correct. Substitute the price for \( p \) in the demand equation. - **Option C:** Solve each equation for \( q \) and set the resulting expressions equal to each other. - **Option D:** Set the two expressions for \( p \) equal to each other. The number of books that are demanded at a price of $20 is \( \_\_\_\_\_\_\_ \). (Round to the nearest whole number as needed.) 2. **Determine the Number of Books Supplied at a Price of $20.** 3. **Graph the Supply and Demand Functions on the Same Axes.** **Graph Explanation:** - The graph comprises two curves representing supply and demand against quantity and price axes. - The supply curve \( p = \frac{1}{2} q^2 \) is upward sloping, indicating that higher prices encourage more supply. - The demand curve \( p = -\frac{1}{2} q^2 + 30 \) is downward sloping, suggesting that lower prices encourage higher demand. - The intersection point of the two curves represents the equilibrium price and quantity.
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