Quantitative Demand Analysis Flashcards
What is the form of a linear demand function and what do the signs determine?
- Qd = α0 + αxPx + αyPy + αMM + αHPH
- Sign before Py determines subistutes/complelemtns
- Sign before M determines normal/inferior
In general, what is the formal for elasticity?
(∆G/G)/(∆S/S) = ∆G/∆S . S/G
What is the point elasticity of OPE?
Point elasticity: ∆Q/∆P . P/Q
What is the total revenue test?
- When demand is elastic, a price increase leads to a decrease in total revenue
- When demand is inelastic, a price increase leads to an increase in total revenue
- When demand is unitary elastic, total revenue is maximised
How can total revenue be maximised using the total revenue test?
To max profit use OPE of demand = αx(Px/Qxd) and solve for P
How does MR relate to elasticity?
- MR = P(1+E/E)
What factors affect OPE?
- Availability of consumption substitutes
- Time/Duration of purchase horizon
- LR more elastic than SR
- Expenditure share of consumers budgets
- Goods that comprise a small percentage of the consumer’s total expenditure will be elastic
What is cross price elasticity?
%∆Qxd / %∆PY
What does cross price elasticity tell us?
- EQXd, PY > 0: substitutes
- EQXd, PY
What is income elasticity?
%∆Qxd / %∆M
What does income elasticity tell us?
- EQXd, M > 0: normal goods
- EQXd, M
What is the shortcut for OPE for a linear demand function?
αx(Px/Qxd)
What is the shortcut for CPE for a linear demand function?
αy(Py/Qxd)
What is the shortcut for Income Elasticity for a linear demand function?
αx(m/Qxd)
What are the components of a regression model function?
- Y = a +bX + e
- a: unknown intercept parameter
- b: unknown slope paramater
- e: random error term with mean zero and st.d σ
What are the components of a least squares regression line?
- Y = â +b̂X + e
- â: least squares estimate of the unknown parameter a
- b̂: least squares estimate of the unknown parameter b
- Both represent the values of a and b that result in the smallest sum of squared errors between a line and the actual data
How is statistical significance evaluated?
- Standard Error
* t-stat
What is standard error?
- How well the fitted equation fits the sample data
- σ̂ = √[SSR/n-2]
What is t-stat?
When |t| > 2, we are 95% confident the true parameter is in the regression is not zero (â and b̂)
How is overal regression line fit evaluated?
- R-Square
* Adjusted R-Square
What is R-Square?
- Coefficient of determination
- Fraciton of the total variation in the dependent variable that is explained by the regression
- R2 = explained variation/total variation = 1 - (SSR/(yi - yavg)
- Ranges between 0 and 1 - values closer to 1 indicate better fit