ECON3520 Chap.4 Production, Investment and Financial Frictions
Production, Investment and Financial Frictions
A production economy adds firms to the household model. The firm borrows and invests in period 1, produces in period 2 and stops when the marginal product of capital equals the gross world interest rate.
This chapter solves a square root technology, explains how productivity and rate shocks shift investment, introduces a collateral ceiling, and traces the direct saving minus investment effect into the current account.
The firm problem is solved before household consumption because investment uses present resources and creates future output.
Diminishing marginal product gives a unique intersection with the gross world financing cost. A productivity improvement raises desired investment, while a higher rate lowers it. The friction block then compares that unconstrained demand with a collateral ceiling: investment follows the marginal-product condition when the ceiling is loose and the financing limit when it binds.
Saving minus investment gives the direct external-balance channel, while a complete interpretation keeps possible household saving responses separate.
What this chapter covers
- 01
Production with diminishing returns
- 02
Marginal product and capital cost
- 03
Square root investment solution
- 04
Productivity shock to investment
- 05
World interest rate channels
- 06
Binding collateral constraints
Worked example · free
Apply a binding collateral ceiling
- 1Realised investment is the minimum of 7 and 4, so the collateral ceiling binds at 4.
- 1Apply current account equals saving minus investment: 9 minus 4 equals 5.
- 1State the condition: the value 5 is the direct effect with national saving held fixed.
Key terms
- Production Function
- A Production Function maps present investment and productivity into future output.
- Diminishing Returns
- Diminishing Returns means each additional unit of investment adds less output than the previous unit.
- Capital Cost
- Capital Cost is the gross repayment, one plus the interest rate, required for one unit of financed investment.
- Investment Schedule
- The Investment Schedule shows how the firm's optimal investment changes with the world interest rate.
- Collateral Constraint
- A Collateral Constraint caps how much a firm can borrow and therefore how much it can invest.
Production, Investment and Financial Frictions FAQ
Why does the firm set marginal product equal to one plus the interest rate?
An additional unit of investment creates marginal future output but must be financed and repaid with interest. The firm invests while the marginal output exceeds that gross cost and stops at equality. Diminishing marginal product makes the intersection unique in the lecture setup.
How does a positive productivity shock affect the current account?
It raises the marginal product of investment, so the firm chooses more investment. Holding household saving fixed, higher investment lowers the current account through saving minus investment. The total equilibrium effect also depends on how higher future output changes the household's consumption and saving choices.
What happens when the collateral constraint binds?
Realised investment equals the collateral ceiling rather than the unconstrained MPK based optimum. A tighter ceiling then directly reduces investment. Conditional on unchanged saving, the current account rises by the amount investment falls, but household saving may also respond in a complete equilibrium.
Exam move
Always solve the firm before solving the household because investment changes the resources left for consumption. Draw a downward marginal product curve and a horizontal gross interest cost, then practise shifting productivity and the rate one at a time. With square root technology, differentiate carefully and substitute the optimal investment back into output.
For a collateral question, calculate the unconstrained optimum, compare it with the cap and state whether the constraint binds. Use current account equals saving minus investment only after saying whether saving is fixed or endogenous. Organise each firm problem as a four-line routine: write profit, differentiate production, equate marginal product to the gross financing cost and test any constraint.
This order makes it harder to confuse the interest rate with one plus the interest rate. For comparative statics, sketch the original and shifted curve on the same axes and identify whether the movement is along marginal product or a shift of it. When collateral appears, calculate the gap between desired and feasible investment because that gap explains both lost future output and the direct saving-minus-investment effect.
In a full economy question, keep firm investment and household saving in separate columns before combining them. End with a conditional statement if saving responses are not specified; do not claim an unambiguous total current-account movement from the investment channel alone.
Working through Production, Investment and Financial Frictions in ECON3520? Sia is AskSia’s AI Economics tutor — ask any ECON3520 Production, Investment and Financial Frictions question and get a clear, step-by-step explanation grounded in how ECON3520 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.