Problem 1
(a) Consumer durables, such as washing machines, are part of the capital stockbut do not generate any financial income for their owners. Why do we include consumer durables in the capital stock? (b) To wash your clothes you can take them to a launderette and spend \(£ 2\) per week indefinitely or buy a washing machine for \(£ 400\). It costs \(£ 1\) per week (including depreciation) to run a washing machine, and the interest rate is 10 per cent per annum. Does it make sense to buy the washing machine? Does this help you answer part (a)?
Problem 2
A bank offers you \(£ 1.10\) next year for every \(£ 0.90\) you give it today. What is the implicit interest rate?
Problem 3
The interest rate falls from 10 to 5 per cent. Discuss in detail how this affects the rental on capital services and the level of the capital stock in an industry in the short and long run.
Problem 4
Suppose a plot of land is suitable only for agriculture. Can the farming industry experience financial distress if there is an increase in the price of land? Is your answer affected if the land can also be used for housing?
Problem 5
Common fallacies Why are these statements wrong? (a) Inflation leads to high nominal interest rates. This reduces the present value of future income. (b) If the economy continues to become more capital intensive, eventually there will be no jobs left for workers to do. (c) Since the economy's supply of land is fixed, it would be supplied even at a zero rental, which should therefore be the equilibrium rental in the long run.
Problem 7
Suppose that the real interest rate in the economy is 4 per cent, while the inflation rate one year from now is known to be 2 per cent. Use the Fisher equation to find the nominal interest rate. Use the nominal interest rate to find the present value of \(£ 100\) one year from now. Now suppose that inflation in one year from now is known to be 4 per cent. How has the present value calculated previously changed? Why?
Problem 9
Suppose you buy a machine that costs \(£ 10000\) today and rent it out. You earn a rent of \(£ 1500\) on that machine every year for four years. After four years the machine can be sold as scrap for \(£ 4000\). Assume that the interest rate is 10 per cent in all four years. What is the present value of the machine? What is the net present value of the machine? Is the investment worthwhile?
Problem 10
Suppose that the demand for capital is given by \(K=20-2 \mathrm{r}\), where \(K\) is capital and \(r\) is the rental rate. In a graph with \(r\) on the vertical axis and \(K\) on the horizontal axis, plot the demand for capital. Suppose that in the short run the supply of capital is fixed at 6 units. In a graph show how the rental rate is determined in equilibrium. An earthquake destroys part of the capital available in the economy. The supply of capital shrinks to 4 units in the short run. What happens to the equilibrium rental rate?
Problem 11
What should be the impact of globalization on assets in fixed supply, particularly land? Can you think of an example in which globalization might induce a fall in land prices?
Problem 13
A firm is producing output using only capital. Its production function is \(Q=10 \mathrm{~K}\) - K2. The firm sells its product in a competitive market at a price of \(£ 2\) and it rents capital from a competitive market at a rental rate of \(r\) per unit of capital. Write down the profit function of the firm and find its capital demand function
