The demand for desk lamp is linear,and the price of desk is
$30.the demand curve for desk lamp then shifts out parallel to itself in response to increase in consumer income.prove that the demand for desk lamps become less price elastic after the shift in the demand curve
To prove that the demand for desk lamps becomes less price elastic after the shift in the demand curve, we need to understand the concept of price elasticity of demand and how it changes with a parallel shift in the demand curve.
Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. Elastic demand is when the quantity demanded is highly responsive to changes in price (elasticity greater than 1), while inelastic demand is when the quantity demanded is less responsive to changes in price (elasticity less than 1).
In this scenario, let's assume the initial demand curve for desk lamps is represented as D1. Since the demand for desk lamps is linear, it implies that the price elasticity of demand for desk lamps initially is constant along the entire demand curve D1.
When consumer income increases, there is typically a parallel shift in the demand curve, meaning that the entire demand curve shifts outward or inward while maintaining the same shape. Let's assume that the demand curve shifts outward parallel to itself, resulting in a new demand curve represented as D2.
Now, let's examine the effect of this shift on the price elasticity of demand. As the demand curve shifts outward, it indicates that consumers are willing to purchase more desk lamps at each price point compared to before. This suggests that the quantity demanded is becoming less responsive to changes in price.
To prove that the demand for desk lamps becomes less price elastic after the shift, we can analyze the percentage change in quantity demanded relative to the percentage change in price before and after the shift.
Before the shift:
- Calculate the initial price elasticity of demand using the initial demand curve D1.
- Compute the percentage change in quantity demanded and price based on the initial price and quantity values.
After the shift:
- Calculate the new price elasticity of demand using the shifted demand curve D2.
- Compute the percentage change in quantity demanded and price based on the post-shift price and quantity values.
Compare the values obtained. If the new price elasticity of demand is smaller (less than 1) compared to the initial elasticity of demand, it demonstrates that the demand for desk lamps becomes less price elastic after the shift.