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Chapter 18 Investment (Types of investment (Residential Investment:…

- - - - Production firms' investment decision
        
        MPK curve is the production firm's capital demand curve because when K = Level of K where MPK = R/P, that means firm cannot increase profit by raising or lowering K (i.e. by renting more/less K).
        
        Production firms maximize profits by choosing K such that MPK = R/P
        MPK is the benefit, R/P is the cost.
        
        Diminishing returns to capital (MPK falls as K falls)
        
        Supply of capital is fixed, thus vertical. Real rental rate (R/P) is determined by intersection of capital demand and supply curves.
      - Cobb-Douglas production function
        Y = A K^𝛂 L^(1-𝛂)
        MPK = dY/dK
        R/P = MPK = 𝛂A(L/K)^(1-𝛂)
        R = rental rate
        P = overall price
      - The equilibrium R/P would increase if:
        
        ↑L (e.g population growth, immigration)
        
        ↑A (e.g. technological improvement)
        
        ↓K (e.g. earthquake, war)
    - - MPK: marginal product of capital
      - Interest rate
    - - Production firms: produce goods and services using capital that they rent
      - Rental firms: own capital; they buy capital and rent it out to production firms
      - Investment in this context is rental firms' spending on new capital goods
    - - Rental firms' investment decision
        
        For rental firms, R/P becomes the benefit instead of the cost, because R/P is the income that rental firms earn from renting the unit of capital to production firms.
        
        Rental firms invest in new capital when benefit of doing so exceeds the cost.
      - Components of the cost of capital:
        
        Interest cost: i x Pk
        i = nominal interest rate
        Pk = purchase price of a unit of capital
        
        Depreciation cost: 𝛿 x Pk
        𝛿 = rate of depreciation
        Pk = nominal price of capital
        
        Capital loss: -∆Pk
        Capital gain ∆Pk > 0 reduces cost of K
      - Nominal cost of capital
        = iPk + 𝛿Pk - ∆Pk
        = Pk ( i + 𝛿 - (∆Pk/Pk) )
        Assume ∆Pk/Pk is inflation π = i - r
        = Pk( r + 𝛿 )
      - Real cost of capital
        = (Pk/P)( r + 𝛿 )
        (Pk/P) = relative price of capital
        r = real interest rate
        𝛿 = depreciation rate
      - Real cost of capital depends positively on:
        
        Real interest rate
        
        Depreciation rate
        
        Relative price of capital