Material on ORB – for your information: Template for test 1 (Jan 17)

2. Material on ORB – for your information: • Template for test 1 (Jan 17) • The New Curriculum -- Essex’s Take • Microeconomics at work – some recent applications of Micro • Cigarette Taxes and Smurfing – “arbitrage” trade in cigarettes

3. Lecture 9: Factor Markets – Capital Reading: Chapter 11 in Begg et al or Chapter 9 in Sloman and Wride AND Notes, Ec111 lecture 9

4. Outline Input Markets with Stocks and Flows The demand for flows – similar analysis to labour markets The demand for stocks -- Net Present Value Criterion Present Values and Internal Rates of Return Equilibrium Investment Demand The Equilibrium Interest Rate Distribution of income across capital and labour

5. Capital and land Physical capital the stock of produced goods which contributes to the production of goods and services (eg, a car for a pizza delivery service). vs. financial capital, which facilitates production but is not itself an input. Land The factor of production which nature supplies. Not itself produced, though can be “augmented” with inputs (such as fertilizer).

6. Other Inputs Resources/ Raw Materials Entrepreneurship

7. Stocks and flows A flow the stream of services that an asset provides during a period (eg. transport services) the rental rate is the cost of using capital services (eg. leasing cost) A stock the quantity of an asset at a point in time (eg. the car’s potential services for you). This may decrease due to depreciation (the loss in value as capital “ages”) the asset price is the sum for which the stock can be bought outright (eg. car’s price on sale)

8. Capital and Labour Input Market Analysis Compared Whereas labour services may only be “rented”, capital services can either be rented or asset that produces these services can be bought. Hence, we analyse both stock and flow equilibria for capital. When capital services are rented (flow analysis), the analysis is analogous to that of labour markets. When capital asset is bought (stock analysis), we must evaluate an investment decision that generates potential costs (up-front, depreciation) and benefits (services) over time. These two analyses are distinct.

9. The Demand and Supply of Capital Services If factors are chosen to maximise profit, then for production depending on capital, K, and Labour, L: Profit = P x Q(K, L) – rK - wL. Increasing capital usage until profit reaches a maximum, we have: r = P x ΔQ(K, L)/ΔK or r = PxdQ/dK = PxMPK So that the cost of each increment of capital, r, just equals the revenue That the increment brings in, PxMPK. We call the revenue that a small amount of capital generates the Marginal Revenue Product (MRPK). r is the marginal cost of capital, MCK For fixed price, P, MRPK decreases due to decreasing marginal returns. In a competitive capital market, r is taken as given (fixed).

10. The Demand and Supply of Capital Services MRPK represents the demand for capital, as it measures the marginal benefit the company earns from capital. £ re MCK MRPK Quantity of capital services per period KD KD is the amount demanded by the firm as a “rent taker”.

11. The Demand and Supply of Capital Services Market Firm SSR £ SLR £ re MCK D MRPK KD K Q, capital services per period Q KD is the amount demanded by the firm as a “rent taker”.

12. The price of a capital asset depends on stream of future services that will be provided. To compare this to the price of the asset (to be paid now), we usually need to evaluate these future services in today’s value. We then compare this aggregate notion of value to the cost – both in today’s terms – and only buy if these benefits outweigh the cost. “Net Present Value Criterion” Analysis of Capital Stocks (Purchase)

13. Present Value • This aggregate notion of the valueof future services – the present value -- depends on • how far into the future the sum accumulates. • the interest rate. • The present value of £1 of service value accrued at some future date is the value that would accumulate to £1 by that future date. • We accumulate at the rate of interest…because that is • the opportunity cost of using money for this investment.

14. Interest and present value (PV) YEAR 0 1 2 At 10% interest rate: Value of £1 lent today in future years: £1 £1.10 £1.21 PV of £1 paid in future year £1 £0.91 £0.83 At 5% interest rate: Value of £1 lent today in future years: £1 £1.05 £1.10 PV of £1 paid in future year: £1 £0.95 £0.91 The Demand and Supply of Capital for Purchase Value in 1 year of £1 received today Value today of £1 paid 1 year in the future

15. £1.10 = £1x(1.10) = £1 x (1+r). £0.91 = £1/(1.10) = £1/(1+r) Why? If I gave you £0.91 today, and you let it accumulate at 10%, then in a year it would give you £0.91x(1.10) = £1. £1.21 = [£1x(1.10)]x(1.10) = £1x(1.10)2= £1x(1+r)2 £0.83 = £1/(1.10)2= £1/(1+r)2 Why? If I gave you £0.83 and you let it accumulate at 10% then in a year it would give you £0.83x(1.10) = £0.91. In another year, that would accumulate to £1. So the present value of a flow of R in year 1 and year 2 would be R/(1+r) + R/(1+r)2

16. Some maths Assuming that the interest rate remains constant, the present value of a future stream of revenues over N years from now, is given by: where Rt is the revenue in year t, i is the interest rate and ∑ is a symbol that means the sum of each year’s discounted earnings. The difference between the present value of the stream of revenues from a given investment minus the actual cost of that investment is called the Net Present Value (NPV).

17. Some maths For example, suppose a firm wants to buy today a machine that costs £8000. The machine can give a revenue of £2000 a year for 4 years. After 4 years the machine can be sold as scrap for £3000 (so it depreciates by £5000 over the 4 years). Assume that the interest rate , r, is 10% in all 4 years. The present value of this stream of future revenues is: Which equals £8388.7. In this case the present value of the future revenues from the machine is higher than the cost of buying the machine. The firm should indeed buy the machine in this case. Note the NPV is £8388.7-£8000 = £388.7

18. Some maths For example, suppose a firm wants to buy today a machine that costs £8000. The machine can give a revenue of £2000 a year for 4 years. After 4 years the machine can be sold as scrap for £3000. What is the effective rate of return on this investment? It is the implicit interest rate in the following expression: Which yields i = 11.8% (about). In this case, the rate of return, i, exceeds the interest rate that could be earned by putting the £8000 into another investment, or 10% in our example, so the firm should make this investment. Investing if i>r is another way of saying the same (NPV) criterion.

19. Rate of return i = r will determine the amount of total investment, as firms select to invest only in projects with positive or zero NPV. r Prevailing rate of interest i = rate of return in investments 1 2 3… Investments The opportunity cost of production for today’s consumption in terms of investment in tomorrow’s consumption is (£1+i)/-£1.

20. The equilibrium real interest rate Demand and Supply of Financial Capital AA' shows the production possibility frontier between current and future consumption: when we devote a lot to Investment, the ROR, i, may be quite low. A' Future consumption by devoting resources to investment, future consumption can be increased. The slope of the frontier has magnitude –(1 + i) where i is the rate of return on investment. (1+i)/-1 A Current consumption

21. The equilibrium real interest rate Given society's preferences between present and future consumption, the optimal position is at E, where the indifference curve UU is at a tangent to the PPF. U E The slope of the red line represents –(1 + r), where r is the real interest rate that balances the productivity of investment and the thriftiness (or impatience!) of consumers. U Slope is the subjective opportunity cost of consuming today vs. tomorrow. A' Future consumption A Current consumption Future = (1+r)Current

22. The functional distribution of income in the UK The distribution of income between the factors of production changed little between 1981-89 and 2006.

23. Summary Capital and land markets have three types of equilibrium issues: -- the equilibrium in the market for flows of capital/land services -- the equilibrium in the market for stocks of capital/land -- the determination of the equilibrium interest rate This is in contrast to labour markets, where only flows are at issue. The decisions about stocks of capital involves evaluating all flows of services from the capital against the cost of the capital in the same time frame. -- usually, this is done with a present value calculation. -- Either the net present value criterion or the internal rate of return criterion is usually used as a decision rule. Shares of income to capital and labour have been very stable over time.