The correct answer is $\boxed{\frac{Y}{K}}$.
The capital-elasticity of output is a measure of how much output changes in response to a change in capital. It is calculated by taking the percentage change in output and dividing it by the percentage change in capital.
In mathematical terms, the capital-elasticity of output is given by:
$$\epsilon_k = \frac{\frac{\Delta Y}{Y}}{\frac{\Delta K}{K}}$$
where $\Delta$ denotes a change in a variable.
If the capital-elasticity of output is greater than 1, then output increases by more than the percentage increase in capital. This means that capital is a relatively important input in the production process.
If the capital-elasticity of output is less than 1, then output increases by less than the percentage increase in capital. This means that capital is a relatively unimportant input in the production process.
If the capital-elasticity of output is equal to 1, then output increases by the same percentage as capital. This means that capital is a neutral input in the production process.
The capital-elasticity of output is an important concept in economics because it helps us to understand how changes in capital affect output. It is also used in economic models to predict how the economy will respond to changes in capital investment.
The other options are incorrect because they do not measure the capital-elasticity of output.
Option A is the marginal product of capital. The marginal product of capital is the additional output that is produced when one more unit of capital is added to the production process.
Option B is the average product of capital. The average product of capital is the total output produced divided by the amount of capital used.
Option C is the capital-output ratio. The capital-output ratio is the amount of capital that is used to produce one unit of output.