1. Lecture 14: Capital Utilisation and the Business Cycle L11200 Introduction to Macroeconomics 2009/10 Reading: Barro Ch.9 24 February 2010

2. Introduction Last time: – Developed model to incorporate labour supply decisions on part of the household – Predictions for procyclicality of employment and hours matched the data Today – Model cannot explain non-employment of factors of production: today consider capital

3. The Problem, Again ‘Equilibrium Business Cycle model’ – Based on idea that capital and labour markets are continually in equilibrium – Excess demand (shortages) or excess supply (unemployment) cannot occur – But unemployment of both labour and capital occur over the business cycle

4. K in the model So far, K has represented both the stock and flow of capital – i.e. K units of capital held by firms were always used in the production – Now change this: firms could hold a stock of capital but choose not to use it – (just like households having a ‘stock’ of labour time available but choosing not to work)

5. Modifying K Replace K in the production function with some proportional κK – κ is the ‘utilisation rate’: the proportion of capital held by households which they actually use – This is very similar to allowing L to vary and become L s instead

6. Demand for Capital Services So now compute how much of the stock of capital K is demanded: ‘capital services’ – Previously calculated demand for capital as a function of real rental cost R/P – If A increased, MPK increased so demand for capital shifted outwards – The same is true for some fixed utilisation rate κ

7. Supply of Capital Services This is the element which now alters: households do not necessarily sell all of their capital to the capital market – Firms might not want to sell all capital if depreciation rate depends on intensity use – i.e. using machines more intensely raises depreciations

8. Supply Decision So now net real income from supplying capital services given by: Rate of return from owning capital is:

9. Supply Decision So rental income is increasing in intensity, but so is depreciation rate – Rate of return is a linear function of κ, i.e. using machines more intensely matches 1:1 to higher rental income – Depreciation is a non-linear function of κ, i.e. more intensive use increases depreciation rate

10. Optimal Capital Supply So optimal supply point maximises net capital rental income – i.e. maximum distance between the two curves – Can analyse impact of changing variables – Most importantly: if R/P increases, encourages more supply of capital – So have a upward-sloping relationship between R/P and capital supply

11. Implication So should find that capital utilisation rate is procyclical – When economy faces positive technology shock, demand for capital services increases – Supply response raises rental rate (and so raises i) and increases capital supply – So capital utilisation and interest rate both move with growth in output

12. Labour Supply With capital, we found that variable capital supply resulted in procyclical utilisation as well as procyclical price for capital – Same pattern as we found for labour supply – Bigger challenge in modelling labour supply is to explain unemployment – Need to introduce some friction in the model which prevents immediate adjustment to new equilibrium

13. Employment over the Business Cycle From lecture 2, we need some basic distinctions – Labour force: everyone who wants to work – Employed: people who want to work and have a job – Unemployed: people who want to work and don’t have a job – Key: variations in employment over the business cycle are not explained by variation in labour force

14. Implications Missing element must be unemployment – Not the case that fluctuations in employment are due to people wanting work more when economy is booming / less when economy is contracting – Instead, when economy is contracting people still want work but cannot find it – This is unemployment: how do we explain it?

15. Summary Capital utilisation varies over the business cycle – Built a model of capital supply based on depreciation being a function of capital intensity – Generated upward-sloping supply and matched the aggregate data Next time: unemployment, the missing element in the model