The owner of Grand Central Bookstore is analyzing the sales of its Health & Fitness magazine section. She finds the equilibrium at 800 magazines per month sold at an average price of $4.75 per magazine. When the price rose to $5.00 each, the quantity sold fell to 725 magazines per month, while the quantity supplied increased to 900 per month.

From the scenario described, answer the questions below:

a. Draw an appropriate graph for Grand Central Bookstore to illustrate the change in the Health & Fitness magazine market position when the price rises to $5.00. (10 pts)

b. Calculate the price elasticity of demand for the Health & Fitness magazines between prices $4.75 and $5.00. Is it elastic or inelastic? How do you know? (10 pts)

c. Calculate the price elasticity of supply for the Health & Fitness magazines between prices $4.75 and $5.00. Is it elastic or inelastic? How do you know based on your answer? (10 pts)

d. The owner also noticed that when she ran a 20% discount on the Health & Fitness magazines, the quantity of nutritious snack bars sold at the checkout register increased by 15%. Calculate the cross elasticity of demand between the two goods. Based on your answer, are they substitutes or complements? Explain why. (10 pts)

The problems posed involve principles of microeconomics such as price elasticity of demand, price elasticity of supply, and cross elasticity of demand. The student would have to draw a graph showing changes in the market for Health & Fitness magazines. Calculations on price elasticities suggest that both demand and supply for these magazines are inelastic. The Health & Fitness magazines and the nutritious snack bar are found to be complementary goods.

Explanation:

The issues at hand involve several economic concepts such as price elasticity of demand, price elasticity of supply and cross elasticity of demand. These concepts fall under the subject of microeconomics, a branch of business or economics.

a. The drawing of the graph would involve showing a shift in the demand curve for the Health & Fitness magazines when the price rises from $4.75 to $5.00, using traditional supply and demand graph conventions.

b. The price elasticity of demand (PED) is calculated by using the formula: PED = (% change in quantity demanded) / (% change in price). With the information given, this results in PED = ((800-725)/800) / ((5-4.75)/4.75) which is approximately -0.42. Since the absolute value is less than 1, it is inelastic, meaning that people's demand is relatively insensitive to price changes.

c. The price elasticity of supply (PES) is calculated in a similar fashion using the formula: PES = (% change in quantity supplied) / (% change in price). Here, it results in PES = ((900-800)/800) / ((5-4.75)/4.75) which is approximately 0.85. Since this is less than 1, it indicates that the supply is relatively inelastic to price changes.

d. The cross elasticity of demand (CED), which measures how the quantity demanded of one good reacts to a change in the price of another good, can be calculated with the formula: CED = (% change in quantity demanded of good 2) / (% change in price of good 1). This gives CED = (15% decrease in snack bar sales) / (20% reduction in magazine price) which is -0.75. The negative sign indicates that these goods are complements, as a price decrease in one good leads to a higher quantity demanded of the other good.

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