Final Answer:
The partial elasticity of foreign demand for our exports with respect to our price level is -1.
Step-by-step explanation:
The given foreign demand function is represented as
, where X is the foreign demand for our exports,
is the foreign income, and P is our price level. To find the partial elasticity of foreign demand with respect to our price level (dX/dP), we differentiate the equation with respect to P.
![\[dX/dP = 0 - 2 * P^(-3) = -2/P^3\]](https://img.qammunity.org/2024/formulas/business/high-school/lid3otcidehl0whklt9tew9squcdfa6u7e.png)
Now, to find the partial elasticity, we use the formula:
![\[E = (dX/dP) * (P/X)\]](https://img.qammunity.org/2024/formulas/business/high-school/zm6bj7xcempgkv6q5u2po03nsrvivhkvn5.png)
Substituting the values:
![\[E = (-2/P^3) * (P/(Y_f^(1/2) + P^(-2)))\]](https://img.qammunity.org/2024/formulas/business/high-school/av3kak00xtptah9xk24c904bj754a93dgy.png)
Simplifying further:
![\[E = -2 * P^(-2) / (Y_f^(1/2) * P + 1)\]](https://img.qammunity.org/2024/formulas/business/high-school/w7ed4jl6jb8srrw9nsl9fpg4krp8bglc1l.png)
To find the partial elasticity at a specific point, you can substitute the given values for
and P. In this case, the elasticity is -1, indicating an inverse relationship between the price level and foreign demand. As our price level increases, foreign demand decreases proportionally.
In economic terms, a partial elasticity of -1 suggests that a 1% increase in our price level would lead to a 1% decrease in foreign demand for our exports, assuming foreign income remains constant. This implies a relatively elastic relationship between our price level and foreign demand.
Full Question:
The Foreign Demand For Our Exports X Depends On The Foreign Income
And Our Price Level
. Find the partial elasticity of foreign demand for our exports with respect to our price level.