ECOS2001 Final Exam notes - StudentVIP2.3 Relative prices • Numeraire/relative pricing: !!!= 1...
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ECOS2001: Final exam Notes Chapter 2: Budget constraint 2.1 Budget constraint • ! ! + ! ! ≤ o Units ( ! , ! ) and prices ( ! , ! ) o Slope/Opportunity cost: ! ! ! ! = − ! ! ! ! o OC: Increasing ! by 1, we reduce ! by ! / ! • Straight line formula: ! = ! ! ! − ! ! ! ! ! • Perfect inflation: price/income rise at same rate then BC same at optimal choice • If p1 declines and p2 same, consumer is at least as well off (lower income bundles available at higher income) 2.1.1 Income change • Higher income: new affordable consumption choices – parallel shift outward 2.1.2 Price change • Good 1 more expensive: increased OC, steeper/pivot inwards • Good 1 less expensive/Good 2 more expensive: lower OC of good 1, flatter/pivot outwards 2.2 Tax, subsidy, rationing • Ad Valorem sales tax o Both p1 and p2 increase 5% (1.05p) or t o Creates income loss through BC o Sales tax levied equivalent to income tax of ! !!! 2.2.1 Food stamp example • BC: F+G=100 ( ! =1 and other goods !"!!" !""#! = 1) o 40 stamps issues: BC enlarged – purchase food and attain 140 units, or spend on others and still get 100 units o Black market: traded for 50c – still afford 140 units of good, or sell for 50c each for extra 20 units of other
Transcript of ECOS2001 Final Exam notes - StudentVIP2.3 Relative prices • Numeraire/relative pricing: !!!= 1...
ECOS2001: Final exam Notes Chapter 2: Budget constraint
2.1 Budget constraint • 𝑝!𝑥! + 𝑝!𝑥! ≤ 𝑚 o Units (𝑥!, 𝑥!) and prices (𝑝!,𝑝!) o Slope/Opportunity cost: !!
!!= − !!
!!
o OC: Increasing 𝑥! by 1, we reduce 𝑥!by 𝑝!/𝑝! • Straight line formula: 𝑥! = !
!!− !!
!!𝑥!
• Perfect inflation: price/income rise at same rate then BC same at optimal choice • If p1 declines and p2 same, consumer is at least as well off (lower income bundles available at higher income)
2.1.1 Income change • Higher income: new affordable consumption choices – parallel shift outward
2.1.2 Price change • Good 1 more expensive: increased OC, steeper/pivot inwards • Good 1 less expensive/Good 2 more expensive: lower OC of good 1, flatter/pivot outwards
2.2 Tax, subsidy, rationing • Ad Valorem sales tax o Both p1 and p2 increase 5% (1.05p) or t o Creates income loss through BC o Sales tax levied equivalent to income tax of !
!!!
2.2.1 Food stamp example • BC: F+G=100 (𝑝!=1 and other goods 𝑝!"!!" !""#! = 1) o 40 stamps issues: BC enlarged – purchase food and attain 140 units, or spend on others and still get 100 units o Black market: traded for 50c – still afford 140 units of good, or sell for 50c each for extra 20 units of other
2.3 Relative prices • Numeraire/relative pricing: !!
!𝑥! +
!!!𝑥! = 1 (set p2 or m=1 as fixed value – doesn’t change BC)
o 2x1 + 3x2 = 12 to 200x1 + 300x2 = 1200 (same constraint)
2.4 BC shapes • Bulk buying discount: curved line
o Slope/− !!!!= −2 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ 20
−1 𝑓𝑜𝑟 𝑥 > 20
• Price penalties: pay tax on excess consumption of good 1 o LHS − !!
!! and RHS /− !!!!
!!
• Negative prices o If p1=2 and m=10 then 2x1 + x2 = 10 or x2 = 2x1 + 10 (budget sets for x2 <
2x1 + 10 • Other o Choice set is intersection of BC sets o Lump sum tax/subsidy shifts BC in/out o Quantity and value (price) tax then price/𝑝! = (1+𝜆) o Quantity (𝑝! − 𝑠) or value [(1-𝜎)𝑝!] subsidy
Chapter 3: Preferences
3.1 Consumer preferences • Strictly: (𝑥!, 𝑥!) ≻ (𝑦!,𝑦!) • Indifferent: (𝑥!, 𝑥!) ∽ (𝑦!,𝑦!) • Weak: (𝑥!, 𝑥!) ≽ (𝑦!,𝑦!)
3.2 Assumptions • Complete: two bundles comparable (x≽y or y≽x) • Reflexive: bundles are good as themselves (𝑥!, 𝑥!) ≽ (𝑥!, 𝑥!) • Transitive: if (𝑥!, 𝑥!) ≽ (𝑦!,𝑦!) and (𝑦!,𝑦!) ≽ (𝑧!, 𝑧!) then (𝑥!, 𝑥!) ≽ (𝑧!, 𝑧!)
3.3 Indifference curves • Bundle x: all bundles equally preferred to x on same IC (indifferent) o Weakly better set: includes IC / Strictly better: not including IC set of bundles preferred weakly to x (including
curve) • Irrationality/distinct levels: IC do not intersect x∽y & x∽z thus y∽z - not possible as on different lines thus y≻z • Discrete goods: unless small amount, continuous is preferred, discrete points
