How do you find the demand function for a Cobb Douglas?
Derived demand for Cobb-Douglas utility a y/x + (1 – a) y'(x) = 0. Solve this for y'(x) to get the slope of the indifference curve: y'(x) = a y(x) / (1 – a) x. The indifference curve through point ‘a’ in figure 11 has slope y'(4) = 0.5 * 8 / 0.5 * 4 = 2.
How do you find the demand function?
Demand Function. A demand function is defined by p=f(x), p = f ( x ) , where p measures the unit price and x measures the number of units of the commodity in question, and is generally characterized as a decreasing function of x; that is, p=f(x) p = f ( x ) decreases as x increases.
What is a in Cobb-Douglas function?
K = capital input (a measure of all machinery, equipment, and buildings; the value of capital input divided by the price of capital) A = total factor productivity. α and β are the output elasticities of capital and labor, respectively. These values are constants determined by available technology.
How do you calculate production function?
The production function is a mathematical equation that calculates the maximum output a firm can achieve with a selected number of inputs (capital, labour, and land). The production function can be calculated using the formula: Q = f(Capital, Land, Labour), where the inputs are a function of the output.
How do you calculate utility bundles?
To find the consumption bundle that maximizes utility you need to first realize that this consumption bundle is one where the slope of the indifference curve (MUx/MUy) is equal to the slope of the budget line (Px/Py) in absolute value terms. You know MUx = Y and MUy = X, so MUx/MUy = Y/X.
What is Cobb Douglas cost function?
The Cobb-Douglas (CD) production function is an economic production function with two or more variables (inputs) that describes the output of a firm. Typical inputs include labor (L) and capital (K). It is similarly used to describe utility maximization through the following function [U(x)].