ECON 352x 1st Edition Exam 2 Study Guide Investment plays a crucial role in economic growth and fluctuates sharply over the business cycle Assumptions 1 Assume the typical firm that produces the economy s output is competitive It takes price of its output P and price of inputs wage rate W and rental rate of capital R as given Firm s actions do not affect prices 2 Firms maximize profits revenue costs P PY WL RK P F K L WL RK Labor Change in Profit Change in Revenue Change in Cost P x MPL W If MPL W P firm can profits by L If MPL W P firm can profits by L Hire labor up to where MPL W P w W P is the real wage in units of output The MPL schedule is the firm s labor demand curve and when MPL is decreasing the labor demand curve is downward sloping Capital Change in Profit Change in Revenue Change in Cost P x MPK R If MPK R P firm can profits by K If MPK R P firm can profits by K Invest capital up to where MPK R P R P is the real rental price of capital also called the user cost of capital uc and is equal to the real interest rate r plus the depreciation rate d uc r d The MPK schedule is the firm s capital demand curve and when MPK is decreasing in K the capital demand curve is downward sloping These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Cost of Capital Rent its entire capital stock from a rental firm which just invests in new capital and rents out the capital firms usually do both Separate cost of renting K and cost of buying I Firm s cost of capital for a unit CoC i PK DPK d PK Pk Purchase price of new investment good i nominal interest rate change in Pk capital gain d rate of depreciation CoC PK i DPK PK d It is typical to assume that DPK PK grows at the rate of inflation and r i inflation or real interest rate is equal to nominal interest rate minus inflation Thus we can write unit nominal cost as PK r d Marginal user cost in real terms uc PK r d P We assume that price of capital PK is equal to P Note that the book defines P K as the real price of capital and uc as the dollar user cost of capital Therefore uc r d Marginal revenue MPK If firms are maximizing profits we therefore get the condition MPK r d This equation determines the desired capital stock that firms have to invest denoted Kd r enters cost of investment in new capital thus the desired capital stock depends on r denoted Kd r Taxes and Cost of Capital If f is the marginal tax rate for firms profits then MPK 1 f R P r d This gives 1 R r d MPK 1 f P 1 f this is the cost of investment in new capital Taxes reduce after tax revenues This requires a higher MPK to pay the same uc r d Taxes combined with the current treatment of inflation affect greatly the after tax returns for consumers Taxes are levied on consumers nominal savings The income tax rate is denoted c After tax nominal returns is iAT iBT 1 c Investment The implied real returns are rBT iBT iBT 1 c where is inflation rAT iAT How is investment determined in equilibrium 1 MPK determines the amount of desired capital Kd r 2 Firms have to invest Id to achieve their desired capital stock Let K0 be the current or initial capital stock Capital depreciates at rate d so d K 0 has to be replaced The desired investment is then determined by Kd K0 d K0 Id Thus the desired investment is Id Kd 1 d K0 Definitions Id Kd 1 d K0 is called Gross Investment Kd K0 is called Net Investment Properties of investment Kd r depends on r thus Id depends on r We write Id r Kd r is decreasing in r thus Id r is decreasing in r Combine all the firms demands for investments to get the aggregate demand for investment Id r is decreasing in r hence the demand for investment is a downward sloping curve Good Market Equilibrium In the goods market equilibrium the total demand for investment must be equal to the economy wide saving In a closed economy Id r Sd r desired savings desired investment The goods market equilibrium yields an optimal level of investment I and and equilibrium interest rate r Terms to know Kd Desired capital stock Id Implied desired investment flow i The nominal market interest rate r The real interest rate d Rate of capital depreciation R P Real rental rate of capital Pk Purchase price of new investment goods DPk Capital gains f c Tax rates on firms and consumers respectively iBT rBT Before tax nominal and real interest rate respectively iAT rAT After tax nominal and real interest rate respectively Inflation rate Ch 6 Growth rise in real GDP per capita Can we grow forever Can we grow richer forever Where does growth come from Solow model tells about GDP over time productive function tells about the GDP today Growth accounting can help us decompose growth and inform us about the sources of growth We can relate the growth rate of output to the growth rates of inputs by the following equation change in Y Y change in A A aK change in K K aL change in L L change in A A is the growth rate of total factor productivity the rest of the equation is the total input growth aK is the elasticity of output with respect to capital aL is the elasticity of output with respect to labor If you know the growth rates DY Y DK K and DL L you can back out The growth rate of TFP DA A A s are called Solow residuals The growth rate of labor productivity DAL AL when you rearrange the equation change in Y L Y L change in A A a K change in K L K L growth rate of GDP per worker growth rate of TFP plus growth rate of capital labor ratio Y L is GDP per employed person K L is the capital labor ratio Growth in Labor L comes from population growth from all sources increases in labor participation Growth in Capital K come from Net investment enabled through saving Growth in TFP A comes from Innovation A large list of forces institutions markets culture Least understood and yet the most important element The 1970 s saw a sharp decrease in TFP due to measuring quality improvements is hard health environment and worker safety regulations and large increase in oil prices Also learning takes time as there was a huge IT revolution Growth Accounting It does not explain …