IS-LM Model Investment Demand Function Shift, Labor and Investment, Tobin Q

Q4a). With this model, we can see how a typical investment demand function in an IS-LM model
might shift. Looking at the net investment function, In(MPK −(r+δ) PK P ), shifts in the
investment function can come either from forces that change the marginal product of capital,
MPK. This include labor, technology, or the overall supply of capital in the economy, or from
changes in the cost of capital, (r +δ) PK P (aside from r, since that represents a shift along the
demand curve).
b). Prn = P·F(K,L)−RK −W L
MPK = ∂F(K,L) ∂K = R P
MPK = αA L K 1−α = R P
K D = (αA) 1 1−α R P − 1 1−α L ⇒ K D = f R P ,L,A −
iPKK | {z } opp. cost − ∆PKK | {z } appr. cost + δPKK | {z } depr. cost
(iPK −∆PK +δPK)K
(iPK − ∆PK ·PK PK +ΔpK)K
(i− ∆PK PK +δ) PKK
R P K −(r +δ) PK P K = R P −(r +δ) PK P K
∆K = In(MPK −(r +δ) PK P )
Kt+1 = (1−δ)Kt +It Kt+1 −(1−δ)Kt = It Kt+1 −Kt +δKt = It ∆K +δK = I In +δK = I𝑀𝑃𝐾 =
𝑃𝑘 𝑃 (
𝑟 +
𝛿)
c). 1/1 (0.1+0.1) = 0.2
0.2=Y
K^0.5. (100^0.5)= 0.2
K^0.5 (10) = 0.2
K^0.5 = 0.02
K= 0.07071
d). Yes, when the price of the product increases that means more profit to the seller. Thus
increasing investment will lead to greater profits.
e). A higher K leads to a lower marginal product of capital, and a lower K leads to a higher
marginal product of capital. Thus, when the rental firm increases its stock of capital, for the
production firm to be willing to rent that much capital, the real rental rate needs to be lower,
since the marginal product will be lower. Thus, we can truly think of this model having a steady
state - if the rental rate is below its steady state level (and thus below the cost of capital), then the