Defines a Cobb Douglas utility function U=∏* _{n}*(

*g*). The Cobb Douglas utility function is equivalent to a CES utility function where the elasticity of substitution is equal to 1. This class is a subclass of

_{n}^{αn}`CES`

, itself a subclass of `Utility`

.## Initialization Parameters

**goods***— list[str]|dict{str:num}, required*Either a list of goods, in which case all exponents will be set to

`1/len(goods)`

, or a dict where the keys are the goods and the values are the corresponding exponents (the*α*s in the formula above). The list may, but does not have to, correspond to the goods registered in_{n}`model.addGood()`

.

## Methods

*Click a method name for more detailed documentation.*

**calculate**( quantities )Calculates the agent's utility on the basis of the quantities entered. Subclasses are required to implement this method and should call the parent function

`super().calculate()`

at the*beginning*. The`model.stocks`

dict can be passed directly to this function.`Utility.calculate()`

only returns the values, and is thus useful for counterfactual calculations. To actually realize utility from consumption, use`Utility.consume()`

instead.**consume**( quantities )Sets

`self.utility`

to the value returned from`self.calculate()`

. The`model.stocks`

dict can be passed directly to this function.**demand**( income, prices )Calculates the total demand for the various goods given some income. See the derivation from the utility function here.

**mrs**( good1, q1, good2, … )Calculates the marginal rate of substitution between two goods. Subclasses are required to implement this method.

**mu**( quantities )Calculates the marginal utilities of the goods in question on the basis of the entered quantities. Many utility functions, including the CES function, are such that the quantities of all goods are necessary to calculate the marginal utility of any good. Subclasses are required to implement this method.

## Properties

**utility***— num*The agent's current level of utility, updated whenever

`Utility.consume()`

is called.Initial value: 0

**elast***— num*Stores the elasticity of substitution.

**coeffs***— dict{str:num}*Stores the coefficients on the goods (

*β*in the CES formula).**exponents***— dict{str:num}*The exponents in the goods (α in the formula above). This property aliases the

`coeffs`

property inherited from the`CES`

class, since the coefficients of a CES utility function become the exponents of a Cobb Douglas function when the elasticity of substitution is 1, and exists mainly for expositional convenience.

## Notes and Examples