Endowments & Intertemporal Allocation Flashcards
What gives rise to labour supply problems?
Time is a limited resource with alternative uses so a consumer faces a trade-off between work (which allows for consumption) and leisure
What are the two approaches to a labour supply problem?
Maximise the utility from consumption and leisure subject to the the amount of consumption determined by that level of leisure
The consumer’s budget is their available hours times the wage rate, consumption x has price p and leisure l has price w so interior optimum will have MUx/p = MUl/w
How could you think of a wage change?
Equating marginal utility to price ratios for consumption and leisure, wage changes correspond to budget set changes as the worker owns their time but must still “pay” for leisure
What axes are used for labour supply curves?
Labour supply against wage rate
Labour supply problems may also require time against consumption axes
How do you translate an endowment to a budget set?
For an endowment bundle ω and corresponding price bundle p, the budget set B = {x | x ≥ 0, x ⋅ p ≤ ω ⋅ p}
Graphically, this will be a line passing through the endowment with slope -p1/p2, with any shifts in price pivoting the BL around the endowment
What can be said about the welfare change from a price decrease for a good with an endowment?
The consumer will be better off (or no worse off) if they were a net demander of the good who’s price fell and will be worse off if they were a net supplier of the now cheaper good
This can be seen graphically by comparing the choice made to what is now available in the budget set and using the logic of revealed preferences
How do intertemporal allocation problems arise?
A consumer may face a tradeoff between consuming now (with borrowing) or consuming later (with saving now)
What is the difference graphically between intertemporal allocation when borrowing is and is not allowed?
When borrowing is not allowed the budget line will extend from the endowment to the future consumption axis, when borrowing is allowed the line will extend to both axes
If a consumer consumes and earns in two periods and can borrow or save at interest rate r, what are the present and future values of their overall income?
Present (in present units): m1 + m2/(1 + r)
Future (in future units): m1(1 + r) + m2
These have nothing to do with preferences (not how much the consumer values these incomes), these only relate to budget set
What is the BL for a consumer consuming and earning in two periods who can save or borrow at interest rate r?
Line from the future value to the present value passing through the endowment with slope -(1 + r) (as if it is ratio of price of present to future consumption)
How can an intertemporal allocation problem be solved?
In the probable case that there is an interior solution, the tangency condition will be met at the optimal allocation so |MRS| = 1 + r
What can be said about the welfare change from an interest rate change in an intertemporal allocation problem?
If the consumer is a lender (saves in the present period) then an increase in the interest rate will make them better off, if the consumer is a borrower then an increase in the interest rate will make them worse off as they will no longer be able to afford their previous optimum unless they switch to being a lender in which case they may be better off
