Quantitative Demand Analysis

Question 1

What is the form of a linear demand function and what do the signs determine?

Answer 1

• Qd = α0 + αxPx + αyPy + αMM + αHPH
• Sign before Py determines subistutes/complelemtns
• Sign before M determines normal/inferior

Question 2

In general, what is the formal for elasticity?

Answer 2

(∆G/G)/(∆S/S) = ∆G/∆S . S/G

Question 3

What is the point elasticity of OPE?

Answer 3

Point elasticity: ∆Q/∆P . P/Q

Question 4

What is the total revenue test?

Answer 4

• 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

Question 5

How can total revenue be maximised using the total revenue test?

Answer 5

To max profit use OPE of demand = αx(Px/Qxd) and solve for P

Question 6

How does MR relate to elasticity?

Answer 6

• MR = P(1+E/E)

Question 7

What factors affect OPE?

Answer 7

• 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

Question 8

What is cross price elasticity?

Answer 8

%∆Qxd / %∆PY

Question 9

What does cross price elasticity tell us?

Answer 9

• EQXd, PY > 0: substitutes

- EQXd, PY

Question 10

What is income elasticity?

Answer 10

%∆Qxd / %∆M

Question 11

What does income elasticity tell us?

Answer 11

• EQXd, M > 0: normal goods

- EQXd, M

Question 12

What is the shortcut for OPE for a linear demand function?

Answer 12

αx(Px/Qxd)

Question 13

What is the shortcut for CPE for a linear demand function?

Answer 13

αy(Py/Qxd)

Question 14

What is the shortcut for Income Elasticity for a linear demand function?

Answer 14

αx(m/Qxd)

Question 15

What are the components of a regression model function?

Answer 15

• Y = a +bX + e
• a: unknown intercept parameter
• b: unknown slope paramater
• e: random error term with mean zero and st.d σ

Question 16

What are the components of a least squares regression line?

Answer 16

• 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

Question 17

How is statistical significance evaluated?

Answer 17

• Standard Error

* t-stat

Question 18

What is standard error?

Answer 18

• How well the fitted equation fits the sample data

- σ̂ = √[SSR/n-2]

Question 19

What is t-stat?

Answer 19

When |t| > 2, we are 95% confident the true parameter is in the regression is not zero (â and b̂)

Question 20

How is overal regression line fit evaluated?

Answer 20

• R-Square

* Adjusted R-Square

Question 21

What is R-Square?

Answer 21

• 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