L4 - Demand and Elasticities

Question 1

What is meant by comparative statics?

Answer 1

The term ‘comparative statics’ is used to refer to the analysis of changes in equilibrium that occur due to some specified change in environment.

Question 2

What is the demand function for Perfect complements?

Answer 2

if U(q₁,q₂) = min(q₁,q₂)

then the demand function for both quantities is as follows:

Y/( p_{1 +}p₂)

Question 3

How is a shift in income represented on a graph?

Answer 3

• keeping prices constant as the budget constraint moves outwards we end up on a higher point on a higher utility curve, connect all these optimal points creates the Income-consumption curve
• This can also be represented as a shift outwards of the demand curve
• If income is plotted against quantity this will create a sloped line called the Engel curve

Question 4

How can we mathematically define a normal and an inferior good?

Answer 4

If H is the quantity of a good, and M is income then:

• dH*/dM > 0 –> Good H is a normal good –> income rises so does consumption
• dH*/dM < 0 Good H is an inferior good –> income rises consumption falls

Question 5

How is a change in my own prices represented on a graph?

Answer 5

• Hold income constant
• As the price of Good X falls (keeping all others constant) we can consume more of it so as the budget contraint pivots outwards, the optimal point rise on each repsectively budget constraint onto a new indifference curve
• This points can be connect to create the price-consumption curve
• When plotting price against quantity for each of the various optimal points we can create an individuals demand curve

Question 6

What does the demand curve for perfect substitutes look like?

Answer 6

• When looking at two different goods:
• When P₁ > P₂ there is no demand for good 1 (vertical line down the axis)
• When P₁ = P₂ demand is equal to Y/P₁ = Y/P₂ –> straight line to this quantity

_- P₁ < P₂ –> indifferent to the amount of good 1 so demand falls line a normal demand curve at Y/P₁

Question 7

How do we mathematically define substitute, complement and independent good?

Answer 7

• If dH*/dp_G > 0 –> Good G and H are substitutes
• If dH*/dp_G​ < 0 –> Good G and H are complements
• If dH*/dp_G​ = 0 –> Good G and good H are indepedent goods –> arent affect be a change of price of either good

(different good)

Question 8

How is a change of a different good represent on a graph?

Answer 8

• as good Y Falls the budget constraint pivots down
• depending on the type of good this can increase or decrease the quantity demanded thus increasing or decreasing the utility gained.

Question 9

How can we mathematically defined an ordinary and a Giffen good?

Answer 9

• If dH*/dp_H < 0 –> Good H is an ordinary good
• If dH*/dp_H > 0 –> Good H is a Giffen good

(change in own price holding other constant)

• normal good is not the same as a ordinary good
• ordinary good –> sees a decrease in demand for an increase in its own prices
• Giffen good –> sees an increase in demand or no fall at all when prices increase

Question 10

What is the income elasiticity of demand?

Answer 10

income elasticity of demand is defined as the % change in demand for good H that follows from a 1% increase in income.

• 𝜼 = (% 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝑯∗ /% 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝑴)

= ((𝝏𝑯∗ /𝑯∗ )x𝟏𝟎𝟎) / ((𝝏𝑴/𝑴)x𝟏𝟎𝟎)

= (𝝏𝑯∗ /𝑯∗ ) /(𝝏𝑴/𝑴)

= (𝝏𝑯∗x𝑴)/(𝝏𝑴x𝑯∗)

= (𝝏𝑯∗ /𝝏𝑴) x (𝑴/𝑯∗)

• The definitions indicate that a good is a normal good if ∂H*/∂M > 0. Hence, we can also suggest that a normal good will have a positive income elasticity, 𝜼>0 (because (M/H*)>0)

Question 11

What Cross-Price Elasticity of Demand?

Answer 11

• The cross-price elasticity of demand for good H (with respect to good G) is defined as the % change in demand for good H that follows from a 1% increase in the price of good G.
• 𝜺_𝑯𝑮 = (% 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝑯∗) /(% 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒑_𝑮)

= (𝝏𝑯∗/ 𝝏𝒑_𝑮) x (𝒑_𝑮/𝑯∗)

• From above, goods G and H will have a positive cross price elasticity if they are substitutes and a negative cross price elasticity if they are complements.
• Busch et al (2004) suggest a 10% increase in the price of cigarettes causes poor families to reduce their demand for food by 17%. Are cigarettes and food substitutes or complements? (Would you still use taxes to reduce smoking?)

Question 12

What is Own-Price Elasticity of demand?

Answer 12

• own-price elasticity of demand is defined as the % change in demand for good H that follows from a 1% increase in the price of good H.
• 𝜺_𝑯𝑯 = (% 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝑯∗)/(% 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒑_𝑯)

= (𝝏𝑯∗/ 𝝏𝒑_𝑯) * (𝒑_𝑯/𝑯∗)

• From above, it follows that good H will have a negative own price elasticity if it is an ordinary good.