The Population Logit Model of the Binary Dependent Variable Y $$\operatorname { Pr } \left( Y = 1 \mid X _ { 1 } \right) = \frac { 1 } { 1 + e ^ { - \left( \beta _ { 0 } + \beta _ { 1 } X _ { 1 } \right) } }$$

question 1

Essay

The population logit model of the binary dependent variable Y with a single regressor is $$\operatorname { Pr } \left( Y = 1 \mid X _ { 1 } \right) = \frac { 1 } { 1 + e ^ { - \left( \beta _ { 0 } + \beta _ { 1 } X _ { 1 } \right) } }$$ Logistic functions also play a role in econometrics when the dependent variable is not a
binary variable.For example, the demand for televisions sets per household may be a
function of income, but there is a saturation or satiation level per household, so that a
linear specification may not be appropriate.Given the regression model $$Y _ { i } = \frac { \beta _ { 0 } } { 1 + \beta _ { 1 } e ^ { - \beta _ { 2 } X _ { i } } } + u _ { i } ,$$ sketch the regression line.How would you go about estimating the coefficients?

---

Definitions:

Oligopoly

A market structure characterized by a small number of large firms dominating the market, leading to limited competition.

Mutually Cancelling Advertising

Mutually cancelling advertising refers to a situation where the competitive advertising efforts of firms negate each other's impact, leading to no significant change in market share.

Economic Efficiency

A state in which resources are allocated in the most beneficial way, maximizing output while minimizing waste and inefficiency.

Oligopolistic Firms

Companies in a market structure where a small number of firms dominate the industry, often leading to less competition.