• Physical capital comprises real assets yielding services to producing firms or consuming households. The main categories of physical capital are plant and machinery, residential structures, other buildings, consumer durables, and inventories. Tangible wealth is physical capital plus land.
• Present values convert future receipts or payments into current values. Because lenders can earn – and borrowers must pay – interest over time, a pound tomorrow is worth less than a pound today. How much less depends on the interest rate. The higher the interest rate, the lower the present value of any future payment.
• Since lending or borrowing cumulates at compound interest, for any given annual interest rate the present value of a given sum is smaller the further into the future that sum is earned or paid.
• The present value of a perpetuity is the constant annual payment divided by the rate of interest (expressed as a decimal fraction).
• Nominal interest rates measure the monetary interest payments on a loan. The inflation-adjusted real interest rate measures the extra goods a lender can buy by lending for a year and delaying purchases of goods. The real rate of interest is the nominal interest rate minus the inflation rate over the same period.
• In the long run, the real interest adjusts to make investment equal to saving, and is determined by the return on firms’ investment and the degree of impatience of households.
• The demand for capital services is a derived demand. The firm’s demand for capital services is its marginal value product of capital curve. Higher levels of the other factors of production and higher output prices shift the derived demand curve up. The industry demand for capital services is less elastic than the horizontal sum of each firm’s curve because it also allows for the effect of an industry expansion in bidding down the output price.
• In the short run the supply of capital services is fixed. In the long run it can be adjusted by producing new capital goods or allowing the existing capital stock to depreciate.
• The required rental is the rental that allows a supplier of capital services to break even on the decision to purchase the capital asset. The required rental is higher, the higher is the interest rate, the depreciation rate or the purchase price of the capital good.
• A rise in the industry wage has two eff ects on the derived demand curve for capital services. By reducing labour input it reduces the marginal physical product of capital. By reducing the industry output it increases the output price. When output demand is very inelastic the latter effect will dominate. When output demand is very elastic the former effect dominates.
• The asset price is the price at which a capital good is bought and sold outright. In long-run equilibrium it is both the price at which suppliers of capital goods are willing to produce and the price at which buyers are willing to purchase. The latter is merely the present value of anticipated future rentals earned from the capital services that the good provides in the future.
• Land is the special capital good whose supply is fixed even in the long run. However, land and capital can move between industries in the long run until rentals on land or on capital are equalized in different industries.

PART TWO Positive microeconomics

• Technology and the ease of factor substitution dictate the very different capital intensity of different industries. Most industries are becoming more capital-intensive over time, but at different rates. Th is reflects the ease with which industries can substitute capital for labour, the rise in wage rates rises relative to capital rentals, and technical advances in different industries.
• The functional distribution of income shows how national income is divided between the factors of production. The share of each factor has remained fairly constant over time. This conceals a rise in the quantity of capital relative to labour, and a corresponding fall in the ratio of capital rentals to labour wages.
• The personal distribution of income shows how national income is divided between different individuals regardless of the factor services from which income is earned. A major cause of income inequality in the UK is a very unequal distribution of income-earning wealth.