When XYZ firm entered the market for good two years back, it kept the price of its product low to attract customers away from its leading competitor. The firm has now established itself and has a market share of 20 percent. The management of XYZ is is planning to increase price of A from the current $6 per unit to $7 per unit, Timothy Walters, the marketing head, however, feels this is not a good idea because it will reduce quantity demanded drastically from the current 1,200 units to 900 units. His colleague and the head of the sales department, Jake Mayers, feels that the quantity demanded would only decline by 250 units. According to Jake, the firm can afford to increase the price because even after the price increase they would still have significant market share. Which of the following, if true, would imply that the firm is operating in the inelastic portion of the demand curve?

a. the rival firm has reduced the price of its product by $1.
b. The $1 increase in price cause the leading competitor's market share to increase substantially.
c. The demand curve is vertical.
d. The demand curve recently shifted such that 20 additional units are demanded at each price level.
e. the quantity demanded declines by 10 percent in response to the $1 price increase

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To determine which option would imply that the firm is operating in the inelastic portion of the demand curve, we need to understand the concept of elasticity.

Elasticity measures how responsive the quantity demanded is to a change in price. If the demand is elastic, a small change in price will result in a proportionally larger change in quantity demanded. If the demand is inelastic, a change in price will lead to a proportionally smaller change in quantity demanded.

Option (e) states that the quantity demanded declines by 10 percent in response to the $1 price increase. This implies that the demand for the product is not very responsive to changes in price. In other words, even with a price increase, the quantity demanded does not decrease significantly. This is an indication of an inelastic demand, as a 10 percent decrease in quantity demanded is relatively small compared to the price increase.

Therefore, option (e) would imply that the firm is operating in the inelastic portion of the demand curve.

To determine which statement implies that the firm is operating in the inelastic portion of the demand curve, let's analyze each option:

a. If the rival firm has reduced the price of its product by $1, it suggests that the two products are substitutes, which could affect the demand for XYZ's product. However, it doesn't directly provide information about the elasticity of demand for XYZ's product.

b. If the $1 increase in price causes the leading competitor's market share to increase substantially, it implies that the demand for XYZ's product is relatively elastic. This option indicates that the firm is not operating in the inelastic portion of the demand curve.

c. If the demand curve is vertical, it means that any change in price will not affect the quantity demanded. This suggests that the demand is perfectly inelastic, indicating that the firm is operating in the inelastic portion of the demand curve.

d. If the demand curve recently shifted such that 20 additional units are demanded at each price level, it indicates an increase in demand. However, it doesn't provide information about the elasticity of demand.

e. If the quantity demanded declines by 10 percent in response to the $1 price increase, it indicates that demand is relatively elastic. This option suggests that the firm is not operating in the inelastic portion of the demand curve.

Therefore, the option that implies that the firm is operating in the inelastic portion of the demand curve is:

c. The demand curve is vertical.