From the case analysis, the price of customized number of plates changed from $25 to $75. The change in price resulted to a reduction in the number of plates ordered by citizens of Texas from 150,000 pieces to 60,000 pieces. The price elasticity calculation resulted to be -0.86. This can be showed in the following details:
The formula to attain this price elasticity is:
The price elasticity of demand calculated on the plates in Texas represents arc price elasticity. Arc price elasticity defines the sensitivity of price between two points on a demand curve. The two points in question here are represented by the changed price and quantity of plates demanded by the applicants.
In the case of Texas State, the rise in price does not lead to a loss. Revenue collected from customized number of plates at a price of $25 adds to $3,750,000. After the rise in price of a single plate to $75, the revenue collected rose to $4,500,000 for the following period. This is different from the reduction in demand from 150,000 pieces to 60,000 pieces. The price elasticity of demand is less than 1 (-0.86). This means an inelastic price elasticity of demand is experienced. The revenue is not affected by the price increase. The percentage change in quantity demanded is smaller than the percentage change in price of the plates. It explains the reason behind the increase in revenue.
The explanation by the director of motor vehicle registration is that a change in price comes as a shallow explanation. In the director’s view, the price rise reduced the demand of plates. This meant that the number of plates produced from that department was reduced at that period. The director considers only the number of pieces produced. With the fact that the state department is not a profit-making organization, serving more residents is their objectives. Therefore, that is why a reduction in the price of plates is relevant to the department. Economically analyzed work means that the decision to reduce the price is wrong.
The change in price only affected the quantity demanded. A negative price elasticity of demand means that the market is inelastic. The effects of price change are more than that of the quantity demanded. According to the figures, -0.86 price elasticity of demand mean that the change in quantity demand does not outweigh the change in price. The higher price change leads to a small change in quantity demanded. This small change results in increase of revenue and lastly profit to the Texas state department of motor vehicle registration. Therefore, the decision by the director to reduce the price is not well informed.
The foot note A depicts the relationship between the quantity demanded and demand. Change in quantity demanded happen along the demand curve. This is caused by the change in price of a unit produced. Calculating the point price elasticity of demand entails different points on the demand curve. Through the use of linear representation of the relationship between quantity demanded and unit price, the point price elasticity of demand is calculated. Arc price elasticity of demand does not use the linear equation. In relation to change in quantity demanded and demand, a shift in demand explains a change in demand. When demand changes, the demand curve shifts.