Term 2 Lecture 6 Flashcards
(18 cards)
Summary, extending the analysis to recognise that the consumer may begin with endowments…
Buy as well as sell goods leads to a richer model. In particular, it suggests a way to model supply of labour and to understand why responses to wage changes may not be as simple as responses to other prices.
New endowment based consumer problem
Max u(q) s.t. P’q < y + p’w
- where w is the initial endowment of goods, so p’w is the value of the initial endowment
- if no endowed income, then the consumer must decide to sell one good to buy another or consume their endowment as it is
- changes in prices affect the slope of the budget constraint, but the endowment remains fixed until consumer decides to trade.
Uncompensated Demand Function w/endowments:
Fi(y,p) = fi(y+p’w,p)
Gross demand vs net demand
- what’s the function looking like?
- gross demand is how much of a good a consumer wants in total
- net demand is the difference between what they consume and what they already own
Z = q-w, so net demand is actually the amount the consumer needs to buy (or sell)
K(y,w,p) = f(y+p’w,p) - w
Effect of income on demand:
Dk(y,w,p)/Dy = Dfi(y+p’w,p)/Dy
- equation states a change in income affects demand the same way, whether it’s from wages or the value of owned goods
Effect of Endowment Changes:
Dk(y,w,p)/Dwj = pi.(Dfi(Y,p)/Dy) - 1, if i = j, if i does not = j, then there’s no minus 1
- essentially, if the endowment of good j increases, the demand for that good i is affected depending on if its the same good or not
- if they are the same, then an increase in the endowment reduces net demand as the consumer already owns more of it
- if they are different, the effect depends on how demand for one good responds to an increase in wealth
Effect of price changes:
Changes in prices have the usual effects, plus an effect due to the change in the value of the individual’s endowment - the endowment income effect
Dki(y,w,p)/Dpj = Dfi(Y,p)/Dpj + wj.Dfi(Y,p)/DY
- first term is the direct price effect, and the 2nd term is the income effect from the endowment
Slutsky equation with endowments:
- take the price affected formula, and substitute the slutsky equation, rearrange
- remember qj - wj = zj
- we get: Dki/Dpj = Dgi/Dpj -zj.Dki/Dy —> the slutsky equation with endowments
So we have the substitution effect, which is negative for normal goods, and the income effect with endowments
Income effect with endowments
- if the person is a net buyer, so qj>wj, the income effect works as usual - higher prices reduce purchasing power, lowering demand
- if the person is a net seller, qj<wj, the price increase makes them richer, potentially increasing demand
Revealed preference implications
A buyer will never become a seller and vice versa
- if someone was willing to sell at price p, they would not become a buyer if the price went up
- if someone was wiling to buy at price p, they would not become a seller if price went down.
Labour-Leisure Tradeoff
- can split this between leisure, h, or labour, l
- earns unearned income, m - from non-work sources and earned income, WL, from working l hours at wage rate w
- they consume a good c at price p
Labour budget constraint
Pc + wh < m + wT
- total spending on consumption and leisure = total income from unearned and total possible earning
- since hours worked, l is just total time minus leisure, l = T-h
Pc /< m + wl
- so total consumption spending is bounded by unearned income and earned income
Whats full income
Total available resources, so m + wT, the max possible income if the person worked all available time
Demand for leisure can be written as
Uncompensated demand function: h = f(M,w,p)
Compensated demand function: h = g(v,w,p)
Slutsky equation for leisure
Df/Dw = Dg/Dw - (h-T)Df/Dm
- substitution effect, so a higher wage makes leisure more expensive
- income effect, a higher wage increases total income, if leisure is a normal good, higher income means people want more leisure
- since the individual sells time, i.e. chooses how much to work, the income effect works in the opposite direction of the substitution effect
Labour supply function
Uncompensated, Marshallian Labour Supply Function:
- l = L(m,w,p) = T - f(m+wT,w,p), since l = T-h, this equation shows that labour supply depends on total wealth M, wages w and consumption prices p
Compensated, Hicksian labour supply function:
- l = Q(v,w,p) = T - g(v,w,p)
Slutsky equation in labour supply
Dl/Dw = DQ/Dw + l.DL/Dm
- total effect, how labour supply changes when wages change
- substitution effect, if wages increase, leisure becomes more expensive
- income effect, higher wages increase income, if leisure is normal, people buy more of it, so usually positive
Backward-Bending Labour Supply Curve
If the substitution effect dominates:
- higher wages means work more, so less leisure and curve slopes up
if the income effect dominates:
- higher wages means work less, so curve slopes down
At LOW wages, sub effect is stronger, so higher wages lead to more work
At HIGH wages, income effect becomes stronger, so higher wages leads to less work
At some critical wage, curve reaches a peak then bends backwards.
