Chapter 17: Investment PDF

# Chapter 17: Investment ## In this chapter, you will learn... - Leading theories to explain each type of investment - Why investment is negatively related to the interest rate - Things that shift the investment function - Why investment rises during booms and falls during recessions ## Three types...

# Chapter 17: Investment ## In this chapter, you will learn... - Leading theories to explain each type of investment - Why investment is negatively related to the interest rate - Things that shift the investment function - Why investment rises during booms and falls during recessions ## Three types of investment - **Business fixed investment:** Businesses' spending on equipment and structures for use in production. - **Residential investment:** Purchases of new housing units (either by occupants or landlords). - **Inventory investment:** The value of the change in inventories of finished goods, materials and supplies, and work in progress. ## U.S. investment and its components This is a line graph showing the total U.S. investment and its components from 1970 to 2005. It is measured in billions of 1996 dollars. The graph shows: - **Total investment:** The total investment in the U.S. over time, fluctuating from 1970 to 2005. - **Business fixed investment:** The investment in business fixed capital. This line is mostly trending upwards. - **Residential investment:** The investment in residential buildings, fluctuating from 1970 to 2005. - **Change in inventories:** The change in the value of inventories from 1970 to 2005, fluctuating between 0 and 250 billion. ## Understanding business fixed investment - The standard model of business fixed investment: **The neoclassical model of investment.** - Shows how investment depends on: - **MPK** - **Interest rate** - **Tax rules affecting firms** ## Two types of firms - For simplicity, assume two types of firms: - **Production firms:** Rent the capital they use to produce goods and services. - **Rental firms:** Own capital; rent it to production firms. - **In this context,** "investment" is the rental firms' spending on new capital goods. ## The capital rental market This is a graph showing the demand and supply of capital in the rental market. - It shows that: - **Production firms** must decide how much capital to rent. - **Competitive firms** rent capital to the point where: - $MPK = R/P$ - **The equilibrium rental rate** is the rental price that equates the demand and supply of capital. - **The graph labels also include:** - **Real rental price R/P** - **Capital supply:** The supply of capital that firms are willing to rent at a given price. - **Capital demand (MPK):** The marginal product of capital, which is the demand for capital at a given price. - **K:** The capital stock, which is the total amount of capital in the economy. ## Factors that affect the rental price - For the **Cobb-Douglas production function**: - $Y = AK^{\alpha}L^{1-\alpha}$ - The **MPK** (and hence equilibrium R/P) is: - $\frac{R}{P} = MPK = \alpha A \left( \frac{L}{K} \right)^{1-\alpha}$ - The equilibrium R/P would increase if: - **K** decreases (e.g., earthquake or war) - **L** increases (e.g., population growth or immigration) - **A** increases (technological improvement, or deregulation) ## Rental firms' investment decisions - Rental firms invest in new capital when the **benefit of doing so** exceeds the cost. - The **benefit (per unit capital)**: - **R/P**, the income that rental firms earn from renting the unit of capital to production firms. ## The cost of capital - **Components of the cost of capital:** - **Interest cost:** $i \times P_{K}$ - where $P_{K}$ = nominal price of capital - **Depreciation cost:** $\delta \times P_{K}$ - where $\delta$ = rate of depreciation - **Capital loss:** $-\Delta P_{K}$ - (a capital gain, $\Delta P_{K}>0$, reduces cost of K) - **The total cost of capital** is the sum of these three parts: - $i \times P_{K} + \delta \times P_{K} - \Delta P_{K} = P_{K}(i+\delta - \frac{\Delta P_{K}}{P_{K}})$ ## The cost of capital - **Nominal cost of capital**: - $i \times P_{K} + \delta \times P_{K} - \Delta P_{K} = P_{K}(i+ \delta - \frac{\Delta P_{K}}{P_{K}})$ - **Example:** Car rental company (capital: cars) - Suppose $P_{K}$ = $10,000, i = 0.10, \delta = 0.20$, and $\frac{\Delta P_{K}}{P_{K}} = 0.06$ - Then the total cost of capital: - Interest cost = $1,000 - Depreciation cost = $2,000 - Capital loss = -$600 - Total cost = $2,400 ## The cost of capital - For simplicity, assume $\frac{\Delta P_{K}}{P_{K}} = \pi$ - Then, the **nominal cost of capital** equals: - $P_{K}(i + \delta - \pi)= P_{K}(r + \delta)$ - And the **real cost of capital** equals: - $\frac{P_{K}}{P}(r + \delta)$ - The real cost of capital depends positively on: - The relative price of capital - The real interest rate - The depreciation rate ## The rental firm's profit rate - A firm's net investment depends on its profit rate: - $Profit Rate = \frac{R}{P} - \frac{P_{K}}{P}(r+\delta) = MPK - \frac{P_{K}}{P}(r + \delta)$ - If the **profit rate > 0,** then increasing K is profitable. - If the **profit rate < 0,** then the firm increases profits by reducing its capital stock. - (Firm reduces K by not replacing it as it depreciates.) ## Net Investment & Gross Investment - **Hence:** - $Net Investment = \Delta K = I_{n}[MPK - \frac{P_{K}}{P}(r+\delta)]$ - Where $I_{n}$ is a function that shows how net investment responds to the incentive to invest. - **Total spending on business fixed investment** equals net investment plus replacement of depreciated K. - **Gross investment = $\Delta K + \delta K$** - **Gross investment = $I_{n}[MPK - \frac{P_{K}}{P}(r+\delta)] + \delta K$** ## The investment function - **The investment function:** - $I = I_{n}[MPK - \frac{P_{K}}{P}(r + \delta)] + \delta K$ - This is a graph showing the investment function. - **An increase in r:** - Raises the cost of capital - Reduces the profit rate - And reduces investment. ## The investment function - **The investment function:** - $I = I_{n}[MPK - \frac{P_{K}}{P}(r + \delta)] + \delta K$ - This is a graph showing the investment function. - **An increase in MPK or a decrease in $\frac{P_{K}}{P}$** - Increases the profit rate - Increases investment at any given interest rate - Shifts the I curve to the right. ## Taxes and investment - **Two of the most important taxes affecting investment:** - **Corporate income tax** - **Investment tax credit** ## Corporate Income Tax: A tax on profits - **Impact on investment depends on definition of "profit":** - In our definition (rental price minus cost of capital), depreciation cost is measured using current price of capital, and the CIT would not affect investment. - But, the legal definition uses the historical price of capital. - If $P_{K}$ rises over time, then the legal definition understates the true cost and overstates profit, so firms could be taxed even if their true economic profit is zero. -_Thus, corporate income tax discourages investment._ ## The Investment Tax Credit (ITC) - The ITC reduces a firm's taxes by a certain amount for each dollar it spends on capital. - Hence, the ITC effectively reduces $P_{K}$ which increases the profit rate and the incentive to invest. ## Tobin's q - **The formula for Tobin's q:** - $q = \frac{Market value of installed capital}{Replacement cost of installed capital}$ - **The components of Tobin's q:** - **Numerator:** The stock market value of the economy's capital stock. - **Denominator:** The actual cost to replace the capital goods that were purchased when the stock was issued. - **How Tobin's q affects investment:** - If $q > 1$, firms buy more capital to raise the market value of their firms. - If $q < 1$, firms do not replace capital as it wears out. ## Relation between q theory and neoclassical theory described above - **The formula for Tobin's q:** - $q = \frac{Market value of installed capital}{Replacement cost of installed capital}$ - **How Tobin's q relates to neoclassical theory:** - The stock market value of capital depends on the current & expected future profits of capital. - If MPK > cost of capital, then profit rate is high, which drives up the stock market value of the firms, which implies a high value of q. - If MPK < cost of capital, then firms are incurring losses, so their stock market values fall, so q is low. ## The stock market and GDP - **Reasons for a relationship between the stock market and GDP:** - A wave of pessimism about future profitability of capital would: - Cause stock prices to fall - Cause Tobin's q to fall - Shift the investment function down - Cause a negative aggregate demand shock - A fall in stock prices would: - Reduce household wealth - Shift the consumption function down - Cause a negative aggregate demand shock - A fall in stock prices might reflect bad news about technological progress and long-run economic growth. This implies that aggregate supply and full-employment output will be expanding more slowly than people had expected. ## The stock market and GDP This is a graph showing the relationship between the stock market and GDP. - The graph shows: - **Real GDP (right scale)**: The percentage change in real GDP from one year earlier. - **Stock prices (left scale)**: The percentage change in stock prices from one year earlier. ## Alternative views of the stock market: The Efficient Markets Hypothesis - **Efficient Market Hypothesis(EMH):** - The market price of a company's stock is the fully rational valuation of the company, given current information about the company's business prospects. - **How the EMH works:** - The stock market is **informationally efficient**. Each stock price reflects all available information about the stock. - This implies that stock prices should follow a **random walk** (be unpredictable), and should only change as new information arrives. ## Alternative views of the stock market: Keynes's "beauty contest" - **Keynes's "beauty contest:"** - This idea is based on a newspaper beauty contest in which a reader wins a prize if he/she picks the women most frequently selected by other readers as most beautiful. - **How Keynes's "beauty contest" relates to the stock market:** - Keynes proposed that stock prices reflect people's views about what other people think will happen to stock prices; the best investors could outguess mass psychology. - Keynes believed stock prices reflect irrational waves of pessimism/optimism ("animal spirits"). ## Alternative views of the stock market: EMH vs. Keynes's beauty contest - **Both views persist.** - There is evidence for the EMH and random-walk theory (see p.498). - Yet, some stock market movements do not seem to rationally reflect new information. ## Financing constraints - **Neoclassical theory** assumes firms can borrow to buy capital whenever doing so is profitable. - **But some firms face financing constraints:** limits on the amounts they can borrow (or otherwise raise in financial markets). - **A recession reduces current profits.** If future profits are expected to be high, investment might be worthwhile. But if a firm faces financing constraints and current profits are low, the firm might be unable to obtain funds. ## Residential investment - The flow of new residential investment ($I_{H}$) depends on the relative price of housing ($P_{H}/P$). - $P_{H}/P$ determined by supply and demand in the market for existing houses. ## How residential investment is determined - This is a graph showing the market for housing, the supply of new housing, and the flow of residential investment. - **(a) The market for housing:** - This graph shows the supply and demand for houses, which determines the equilibrium price of houses. - **(b) The supply of new housing:** - This graph shows the relationship between the price of new housing and the flow of new residential investment. - The equilibrium price of houses determines the flow of residential investment. ## How residential investment responds to a fall in interest rates - This is a graph showing how a fall in interest rates affects the market for housing, the supply of new housing, and the flow of residential investment. - **(a) The market for housing:** - When interest rates fall, the demand for housing increases, leading to higher equilibrium prices. - **(b) The supply of new housing:** - When interest rates fall, the supply of new housing increases. - This increase in housing supply leads to a higher flow of residential investment. ## The tax treatment of housing - The tax code, in effect, subsidizes home ownership by allowing people to deduct mortgage interest. - The deduction applies to the nominal mortgage rate, so this subsidy is higher when inflation and nominal mortgage rates are high than when they are low. - Some economists think this subsidy causes over-investment in housing relative to other forms of capital. - But eliminating the mortgage interest deduction would be politically difficult. ## Inventory investment - Inventory investment is only about 1% of GDP. - Yet, in the typical recession, more than half of the fall in spending is due to a fall in inventory investment. ## Motives for holding inventories - **1. Production smoothing:** Sales fluctuate, but many firms find it cheaper to produce at a steady rate: - When sales < production, inventories rise. - When sales > production, inventories fall. - **2. Inventories as a factor of production:** Inventories allow some firms to operate more efficiently: - Samples for retail sales purposes - Spare parts for when machines break down - **3. Stock-out avoidance:** To prevent lost sales when demand is higher than expected. - **4. Work in process:** Goods not yet completed are counted in inventory. ## The Accelerator Model - A simple theory that explains the behavior of inventory investment, without endorsing any particular motive. ## The Accelerator Model - **Notation:** - N = stock of inventories - $\Delta N$ = inventory investment - **Assume:** - Firms hold a stock of inventories proportional to their output: $N = \beta Y$. - Where $\beta$ is an exogenous parameter reflecting firms' desired stock of inventory as a proportion of output. ## The Accelerator Model - **Result:** - $\Delta N = \beta \Delta Y$ - Inventory investment is proportional to the change in output: - When output is rising, firms increase inventories. - When output is falling, firms allow their inventories to run down. ## Evidence for the Accelerator Model This is a graph showing the relationship between change in real GDP and inventory investment: - The graph shows: - **Inventory investment (billions of 1996 dollars):** The change in inventory investment over time. - **Change in real GDP (billions of 1996 dollars):** The change in real GDP over time. - The graph indicates that **a positive relationship** exists between these two variables. ## Inventories and the real interest rate - The opportunity cost of holding goods in inventory: The interest that could have been earned on the revenue from selling those goods. - Hence, inventory investment depends on the real interest rate. - **Example:** High interest rates in the 1980s motivated many firms to adopt just-in-time production, which is designed to reduce inventories. ## Chapter Summary - **1. All types of investment depend negatively on the real interest rate.** - **2. Things that shift the investment function:** - Technological improvements raise MPK and raise business fixed investment. - Increase in population raises demand for, price of housing, and raises residential investment. - Economic policies (corporate income tax, investment tax credit) alter incentives to invest. ## Chapter Summary - **3. Investment is the most volatile component of GDP over the business cycle:** - Fluctuations in employment affect the MPK and the incentive for business fixed investment. - Fluctuations in income affect demand for, price of housing and the incentive for residential investment. - Fluctuations in output affect planned & unplanned inventory investment.