ECON3520 Chap.3 Intertemporal Consumption and Current Account Shocks
Intertemporal Consumption and Current Account Shocks
The two period household model explains current account movements through consumption smoothing. A present value budget constraint defines what can be consumed, an indifference curve tangency selects the preferred allocation, and the world rate prices transfers across time.
This chapter solves the log utility case, compares temporary with permanent shocks, converts terms of trade into purchasing power, and evaluates interest rate and capital control mechanisms.
Geometry and algebra describe the same choice. The budget-line slope records the world return available to a small economy, while the tangency condition selects the preferred affordable bundle.
Under log utility the model yields a compact consumption rule, after which trade balances, current accounts and closing assets can be recovered. Comparative statics are organised by persistence: a temporary shock invites borrowing or saving to smooth consumption, whereas a permanent shock changes lifetime resources more strongly.
Terms of trade and borrowing restrictions enter by changing real resources or the feasible set.
What this chapter covers
- 01
Present value budget constraint
- 02
Indifference curves and tangency
- 03
Log utility allocation
- 04
Temporary and permanent output shocks
- 05
Terms of trade and information
- 06
World rates and capital controls
Worked example · free
Solve consumption after a temporary output loss
- 1Lifetime resources equal 8 plus 12, which is 20.
- 1With equal log weights and a zero rate, split resources evenly: C1 equals C2 equals 10.
- 1TB1 and CA1 equal 8 minus 10, which is minus 2, so borrowing smooths the temporary loss.
Key terms
- Endowment Economy
- An Endowment Economy gives households output directly and contains no productive investment technology.
- Budget Line
- The Budget Line contains consumption pairs whose present value equals lifetime resources.
- Indifference Curve
- An Indifference Curve contains consumption pairs that deliver the same utility.
- Consumption Smoothing
- Consumption Smoothing uses borrowing or saving to avoid making consumption track temporary income movements one for one.
- Capital Control
- A Capital Control restricts cross border asset choices, such as a prohibition on borrowing from abroad.
Intertemporal Consumption and Current Account Shocks FAQ
What determines the slope of the intertemporal budget line?
The slope is minus one plus the interest rate. Giving up one unit of present consumption releases resources that become one plus the interest rate units of future consumption. A higher rate therefore makes the line steeper in a graph with future consumption on the vertical axis.
Why does a temporary negative shock cause borrowing?
Future output remains unchanged, so lifetime resources fall by less than current output. The household protects present consumption by borrowing against period 2 income. Consumption falls less than present output, and the resulting gap appears as a trade and current account deficit.
Why can a capital control lower welfare while removing a deficit?
The prohibition forces a household that prefers to borrow back to its endowment allocation. Trade balances become zero, so the external target is reached, but the chosen bundle lies on a lower indifference curve than the unconstrained optimum. The welfare conclusion is conditional on the lecture model's assumptions.
Exam move
Draw the graph and solve the equations together. Label the budget slope, the tangency and the endowment point, then use the same symbols in the algebra. For log utility, practise deriving the consumption ratio and splitting present value wealth. Turn every shock question into a chain from persistence to lifetime resources to consumption smoothing to the current account.
For terms of trade, convert export output into import good units before solving. For rate shocks, keep the firm's cost channel separate from household substitution and income effects. For capital controls, report the accounting target and welfare consequence separately. Build a small comparison table for temporary losses, permanent losses, interest-rate changes and terms-of-trade movements.
For each shock, record what changes in present value wealth, whether the budget-line slope moves, how consumption responds and which current-account sign follows. Redraw the endowment point and optimum rather than relying only on verbal intuition. In numerical work, calculate present value resources once, keep extra decimal places until the final line and verify that discounted consumption equals discounted resources.
If a borrowing restriction binds, solve the unconstrained allocation first so the direction of the distortion is explicit. A complete policy answer should name the constrained choice, the resulting external balance and the welfare comparison, without treating a zero deficit as automatic evidence of improvement.
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