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C. Let u(x,.x,) =x? x? , the price of x1 equal p1, and the price of X2 equal p2. Income equals M. Derive individual demand curves for x1 and x2 in terms of income and prices. D. What are optimal quantities if pı=4, p2=2, and M equals $1,000?

C. Let u(x,.x,) =x? x? , the price of x1 equal p1, and the price of X2 equal p2. Income equals M. Derive individual demand curves for x1 and x2 in terms of income and prices. D. What are optimal quantities if pı=4, p2=2, and M equals $1,000?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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please answer question C & D

**Economic Problem Set** **B. Market Demand Curve** Graphically derive the market demand curve for \( x_1 \) in a universe with only two economic agents (individuals). **C. Individual Demand Curves** Let \( U(x_1, x_2) = x_1^{\frac{1}{2}} x_2^{\frac{1}{2}} \), the price of \( x_1 \) equal \( p_1 \), and the price of \( x_2 \) equal \( p_2 \). Income equals \( M \). Derive individual demand curves for \( x_1 \) and \( x_2 \) in terms of income and prices. **D. Optimal Quantities** What are the optimal quantities if \( p_1 = 4 \), \( p_2 = 2 \), and \( M \) equals $1,000?
Transcribed Image Text:**Economic Problem Set** **B. Market Demand Curve** Graphically derive the market demand curve for \( x_1 \) in a universe with only two economic agents (individuals). **C. Individual Demand Curves** Let \( U(x_1, x_2) = x_1^{\frac{1}{2}} x_2^{\frac{1}{2}} \), the price of \( x_1 \) equal \( p_1 \), and the price of \( x_2 \) equal \( p_2 \). Income equals \( M \). Derive individual demand curves for \( x_1 \) and \( x_2 \) in terms of income and prices. **D. Optimal Quantities** What are the optimal quantities if \( p_1 = 4 \), \( p_2 = 2 \), and \( M \) equals $1,000?
### Demand Theory **3. Demand Theory:** **A. From the indifference curve/budget constraint diagram, derive the individual's demand curve for \( x_1 \).** In this section, students will learn how to derive the demand curve for a specific good \( x_1 \) using the concepts of indifference curves and budget constraints. The indifference curve represents various combinations of two goods that provide the consumer with the same level of satisfaction. The budget constraint illustrates the combinations of these goods that the consumer can afford given their income and the prices of the goods. To derive the demand curve for \( x_1 \), follow these steps: 1. **Graph the Indifference Curves and Budget Constraint:** - Plot the budget line based on the consumer's income and the prices of the two goods. - Draw the indifference curves that represent the consumer's preferences. 2. **Find the Consumer's Equilibrium Point:** - Identify the point where the highest attainable indifference curve is tangent to the budget line. This point indicates the optimal combination of the two goods that maximizes the consumer's utility given their budget constraint. 3. **Vary the Price of \( x_1 \):** - Change the price of \( x_1 \) and plot the new budget line. - Determine the new equilibrium point by locating the tangent point between the new budget line and an indifference curve. 4. **Plot the Demand Curve:** - Record the quantity of \( x_1 \) at different prices. - Draw a graph with the price of \( x_1 \) on the vertical axis and the quantity demanded of \( x_1 \) on the horizontal axis. - Connect the points to form the demand curve. This process helps to visualize how changes in the price of \( x_1 \) affect the consumer’s purchasing decisions and allows for the derivation of the demand curve for \( x_1 \).
Transcribed Image Text:### Demand Theory **3. Demand Theory:** **A. From the indifference curve/budget constraint diagram, derive the individual's demand curve for \( x_1 \).** In this section, students will learn how to derive the demand curve for a specific good \( x_1 \) using the concepts of indifference curves and budget constraints. The indifference curve represents various combinations of two goods that provide the consumer with the same level of satisfaction. The budget constraint illustrates the combinations of these goods that the consumer can afford given their income and the prices of the goods. To derive the demand curve for \( x_1 \), follow these steps: 1. **Graph the Indifference Curves and Budget Constraint:** - Plot the budget line based on the consumer's income and the prices of the two goods. - Draw the indifference curves that represent the consumer's preferences. 2. **Find the Consumer's Equilibrium Point:** - Identify the point where the highest attainable indifference curve is tangent to the budget line. This point indicates the optimal combination of the two goods that maximizes the consumer's utility given their budget constraint. 3. **Vary the Price of \( x_1 \):** - Change the price of \( x_1 \) and plot the new budget line. - Determine the new equilibrium point by locating the tangent point between the new budget line and an indifference curve. 4. **Plot the Demand Curve:** - Record the quantity of \( x_1 \) at different prices. - Draw a graph with the price of \( x_1 \) on the vertical axis and the quantity demanded of \( x_1 \) on the horizontal axis. - Connect the points to form the demand curve. This process helps to visualize how changes in the price of \( x_1 \) affect the consumer’s purchasing decisions and allows for the derivation of the demand curve for \( x_1 \).
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