Econ 102 Homework 2

Econ 102homework 2

Use the graph below to answer the following questions. (26 points) a. What is the absolute value of the price elasticity of demand between P=100 and P=80? (5 points) i. Based on the value you calculated, is demand elastic, inelastic, or unit elastic? (4 points) ii. What does the value you calculated imply about the relationship between price and quantity demanded? (4 points) b. What is the absolute value of the price elasticity of demand between P=40 and P=20? (5 points) i. Based on the value you calculated, is demand elastic, inelastic, or unit elastic? (4 points) ii. What does the value you calculated imply about the relationship between price and quantity demanded? (4 points)

Use the graph below to answer the following questions. (36 points – each part is worth 4 points) a. Elasticity values are greater than 1 in absolute value in the portion of the graph described by letter _____. b. Elasticity values are less than 1 in absolute value in the portion of the graph described by letter _____. c. Elasticity values are exactly equal to 1 in absolute value in the portion of the graph described by letter _____. d. The inelastic portion of the graph is the area described by letter _____. e. The elastic portion of the graph is the area described by letter _____. f. The unit elastic portion of the graph is the area described by letter _____. g. Total revenue is maximized over the portion of the graph described by letter _____. h. Total revenue is increasing when price increases over the portion of the graph described by letter _____. i. Total revenue is decreasing when price increases over the portion of the graph described by letter ____.

Suppose the demand for guitars in State College is given by Qd = 8,000 – 10P where Qd is the quantity demanded, and P is the price of guitars. Also, suppose the supply of guitars is given by Qs = 30P – 2000, where Qs is the quantity supplied of guitars. (38 points) a) Calculate the equilibrium price of guitars and the equilibrium quantity of guitars in State College. Show your work. (10 points) b) Suppose the actual price of guitars is $500. Determine if there is a shortage, a surplus, or if the market is in equilibrium at a price of $500. If there is a shortage or surplus, calculate how much the shortage or surplus is. (8 points) c) Given your answer to b), is the price of guitars likely to rise, fall, or stay the same? (4 points) d) Suppose guitars and guitar strings are complements. Draw a graph indicating what will happen in the market for guitar strings if the price of guitars decreases. Be sure to label your graph carefully, putting Price on the vertical axis and Quantity on the horizontal axis. You do not need to have actual numbers on this graph, but you should clearly indicate how the decrease in the price of guitars will affect the market for guitar strings, and what will happen to the equilibrium price and quantity of guitar strings. (16 points)

Paper For Above instruction

Economic analysis of consumer demand and market dynamics offers crucial insights into how prices influence the quantity of goods demanded and supplied. This paper explores several fundamental concepts: price elasticity of demand, the relationship between elasticity and total revenue, and the interdependence of markets for complementary goods such as guitars and guitar strings. Through comprehensive calculations, graphical analysis, and theoretical explanations, we examine how susceptible demand is to price changes, how market equilibrium is determined, and what the implications are for market participants.

Price Elasticity of Demand and Its Interpretation

Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. Generally expressed as the percentage change in quantity demanded divided by the percentage change in price, PED helps categorize demand as elastic, inelastic, or unit elastic. When the absolute value of PED exceeds 1, demand is elastic; if less than 1, demand is inelastic; and if equal to 1, demand is unit elastic.

Between P=100 and P=80, the absolute value of PED can be calculated using the midpoint formula. Assuming the corresponding quantities from the graph are Q1 and Q2, PED = [(Q2 - Q1) / ((Q1 + Q2)/2)] / [(P2 - P1) / ((P1 + P2)/2)]. If, for example, the quantity demanded drops from 50 to 40 as the price decreases from 100 to 80, then PED = [(40 - 50) / (45)] / [(80 - 100) / (90)] = (-10 / 45) / (-20 / 90) = (-0.2222) / (-0.2222) = 1. Thus, demand is unit elastic in this range, implying that percentage changes in price result in proportional percentage changes in quantity demanded. Similar calculations for the P=40 to P=20 range might show a different elasticity, potentially indicating a more elastic demand if the percentage change in quantity demanded is larger relative to price change.

Demand Elasticity in Different Price Ranges

Graphical analysis indicates that at higher prices, demand tends to be less responsive (inelastic), whereas at lower prices, demand becomes more elastic. Elasticity values greater than 1 suggest consumers are highly responsive to price changes, leading to significant changes in quantity demanded. Conversely, when elasticity is less than 1, demand is relatively insensitive to price variations. The point where elasticity equals 1 signifies the unit elastic range, where total revenue is maximized because proportional changes in price and quantity cancel out.

The inelastic segment of the demand curve is where price increases lead to less than proportional decreases in quantity demanded, thus increasing total revenue. Conversely, the elastic segment experiences a decrease in total revenue when prices climb because the drop in quantity demanded outweighs the price increase. The unit elastic point optimally maximizes total revenue, as the elasticities balance out.

Market Equilibrium for Guitars

Given the demand function Qd = 8,000 – 10P and supply function Qs = 30P – 2000, the equilibrium price and quantity are found where quantity demanded equals quantity supplied. Setting Qd equal to Qs:

8,000 – 10P = 30P – 2000

130P = 10,000

P = 10,000 / 130 ≈ $76.92

Substituting P back into the demand equation:

Qd = 8,000 – 10 * 76.92 ≈ 8,000 – 769.2 ≈ 7,230.8

Thus, the equilibrium price is approximately $76.92, and the equilibrium quantity is about 7,231 guitars (rounded). This ensures that the market clears, with no surplus or shortage.

Market Conditions at a Price of $500

At a price of $500, analyze the quantities demanded and supplied:

Qd = 8,000 – 10 * 500 = 8,000 – 5,000 = 3,000

Qd = 30 * 500 – 2000 = 15,000 – 2000 = 13,000

Since Qs (13,000) exceeds Qd (3,000), there is a surplus of:

13,000 – 3,000 = 10,000 guitars

This surplus indicates that the market cannot sustain a price so high without excess supply—buyers will not purchase all available guitars, leading to downward pressure on prices.

Price Adjustment Expectations

Given the surplus at $500, it is likely that prices will fall as sellers reduce prices to clear excess stock. Market forces tend to push the price down toward the equilibrium level, approximately $76.92, increasing demand and decreasing supply at higher prices. Over time, this adjustment restores market balance.

Impact of Decreased Price on Complementary Market

The market for guitar strings is interconnected with that of guitars; as guitars become cheaper, more consumers are likely to purchase guitars, increasing the demand for guitar strings. Graphically, this shift in demand would be represented by a rightward shift of the demand curve for guitar strings, increasing the equilibrium price and quantity. This demonstrates the principle that a decrease in the price of a good can stimulate increased consumption of complementary goods, thereby affecting their markets.

Conclusion

Understanding price elasticity, equilibrium analysis, and market interdependencies are essential for interpreting how markets respond to changes in price. The calculations illustrate the responsiveness of demand at different price levels, while the analysis of the guitar market exemplifies the dynamic process that governs market equilibrium and the ripple effects across related markets. Such analyses are fundamental for economic decision-making by producers, consumers, and policymakers alike.

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