Elasticity
a) Find the elasticity of the demand function q + 2p = 5000 when p = $1000, and q = 3000.
b) How would revenue be affected by a price increase?
dq/dp=-2
E= p/q * dq/dp= 1/3 * -2=-2/3
so if you increased prices, demand decreases.
To find the elasticity of the demand function, q + 2p = 5000, when p = $1000 and q = 3000, we need to use the formula for price elasticity of demand, which is given by:
E = (dq/dp) * (p/q)
where E is the elasticity, dq/dp is the derivative of q with respect to p, p is the price, and q is the quantity demanded.
a) Find the elasticity of the demand function q + 2p = 5000 when p = $1000, and q = 3000:
To find the derivative dq/dp, we need to differentiate the demand function with respect to p. By differentiating q + 2p = 5000 with respect to p, we get:
2 + dq/dp = 0
Rearranging the equation, we have:
dq/dp = -2
Now, substituting the values p = $1000 and q = 3000 into the formula for elasticity, we get:
E = (-2) * (1000/3000) = -2/3
Therefore, the elasticity of the demand function when p = $1000 and q = 3000 is -2/3.
b) How would revenue be affected by a price increase:
To understand how revenue is affected by a price increase, we need to know the relationship between price, quantity demanded, and revenue. Revenue is calculated by multiplying the price of a product by the quantity demanded, that is:
Revenue = Price * Quantity Demanded
When there is a price increase, the quantity demanded usually decreases. However, whether revenue increases or decreases depends on the price elasticity of demand.
If the demand is elastic (elasticity > 1), then a price increase would cause the revenue to decrease. This happens because the decrease in quantity demanded exceeds the increase in price, resulting in a decline in total revenue.
If the demand is inelastic (elasticity < 1), then a price increase would cause the revenue to increase. This happens because the decrease in quantity demanded is relatively smaller than the increase in price, leading to a rise in total revenue.
If the demand is unitary elastic (elasticity = 1), then a price increase would not affect the revenue. The increase in price is exactly offset by the decrease in quantity demanded, resulting in no change in total revenue.
Therefore, the impact of a price increase on revenue depends on the price elasticity of demand.