EF5472 Chap.2 Classical General Equilibrium
Classical General Equilibrium
Build the static economy in the right order
Technology and fixed factor endowments determine output before prices allocate it. Competitive firms hire capital and labour until marginal products equal real factor prices. With Cobb-Douglas technology and constant returns, the exponents become factor income shares and payments exhaust output.
Households divide disposable income between consumption and saving, while firms reduce desired investment as the real interest rate rises. Goods-market clearing makes saving equal investment.
Fiscal changes therefore move national saving, the clearing interest rate and investment within this closure, rather than changing supply-determined output.
Keep production, distribution and allocation separate
A strong solution moves through three closures without changing assumptions halfway. First insert the fixed endowments into the production function to obtain full-employment output.
Next differentiate with respect to each input, impose competitive factor pricing and check that total capital and labour payments exhaust output when constant returns applies. Only then compute disposable income, consumption and national saving.
The real interest rate belongs to the final market-clearing step: solve it from desired investment equal to saving, not from the production function's rental rate unless a question explicitly connects the two returns. For fiscal comparative statics, hold the model's productive capacity fixed, trace the change in private or public saving, find the new clearing rate and state the investment crowding-out result.
Always report which variable absorbs the shock. In this static classical closure it is the interest rate and demand composition, not output. If an answer obtains a change in output, identify the extra friction or variable endowment that would be needed to support it. Finish with a payment audit, a goods-market audit and units for any rate expressed in percentage points.
What this chapter covers
- 01
Production functions
- 02
Diminishing marginal products
- 03
Competitive factor pricing
- 04
Cobb-Douglas income shares
- 05
National saving
- 06
Fiscal crowding out
Worked example · free
Price factors and close the goods market
- 4Compute output and both marginal products.
- 3Verify factor payments exhaust output.
- 3Equate saving with desired investment.
Key terms
- Constant Returns
- A technology property under which scaling every input by the same factor scales output proportionally.
- Marginal Product
- The extra output produced by an additional unit of one factor with other inputs fixed.
- Factor Share
- The portion of aggregate income received by one production input.
- National Saving
- Output not used for private consumption or government purchases in a closed economy.
- Crowding Out
- The fall in investment caused by lower national saving and a higher clearing real interest rate.
- User Cost
- The real financing and depreciation cost of holding productive capital.
Classical General Equilibrium FAQ
Why does demand not determine output in the classical model?
Capital, labour and technology are fixed before spending decisions are allocated, so the production function already pins down output. Prices distribute income and the real interest rate divides output among uses. Demand affects output only after a later model adds a friction or unused-capacity mechanism.
Why do Cobb-Douglas exponents equal income shares?
In a competitive factor market, the rental rate and wage match their respective marginal products. Multiplying the Cobb-Douglas marginal product by the factor quantity produces its exponent times output. Constant returns makes the exponents sum to one, so capital and labour payments exhaust output with zero pure profit.
How does a rise in government purchases crowd out investment?
With output fixed, higher government purchases reduce national saving one-for-one when taxes and consumption are unchanged. The saving schedule shifts left, the real interest rate rises and desired investment falls until it equals the smaller saving supply. The result depends on the classical closure rather than an accounting identity alone.
Exam move
Redraw the model as three stacked markets: production and factor pricing at the top, household and government saving in the middle, and investment clearing at the bottom. Work a Cobb-Douglas example until output, marginal products, total payments and shares reconcile without looking at notes.
Then practise three fiscal shocks: purchases financed by unchanged taxes, a tax change under the reduced-form consumption function, and a temporary debt-financed tax cut interpreted by a forward-looking household. For each, write which object is fixed and which curve moves. End every solution by checking that saving equals investment and by stating why output did or did not change in the chosen closure.
Keep the capital rental price visually distinct from the intertemporal interest rate throughout every derivation and comparative-static explanation.
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