Krizalid said:It's pretty straightforward. I'll do the first one for you. We have $y_k=Aak^{a-1}$ (because the other term doesn't have a $k$ since it's the partial derivative), and $y_k$ denotes the partial derivative respecto to $k.$
Try the other one and substitute.
A partial derivative in economics is a mathematical concept used to measure the rate of change of a specific variable in relation to another variable, while holding all other variables constant. It is a useful tool for analyzing how changes in one variable affect another variable, and is commonly used in economic models and theories.
To calculate a partial derivative in economics, you first need to determine the function that represents the relationship between the variables of interest. Then, you take the derivative of that function with respect to the variable you want to measure, while holding all other variables constant. This will give you the partial derivative of that variable.
The main purpose of using partial derivatives in economics is to better understand the relationships between different variables in an economic model or theory. By calculating the partial derivatives of these variables, economists can determine how changes in one variable will affect another variable, and make predictions about the behavior of the economic system.
Yes, partial derivatives can be negative in economics. This means that there is an inverse relationship between the two variables being analyzed - as one variable increases, the other decreases. This is a common occurrence in economic models and can provide valuable insights into the behavior of the system.
Partial derivatives are used in a variety of ways in real-world economic analysis. They can be used to determine the marginal effects of different economic policies or changes in market conditions, to forecast future trends, and to evaluate the efficiency of various economic systems. They are a powerful tool in economic analysis and play a crucial role in understanding and predicting economic behavior.