ECON 2103A: Macroeconomics Assignment 1 - IS-LM, Consumption

This assignment solution for ECON 2103A covers several key macroeconomic concepts. Question 1 addresses consumption theories, explaining Keynes' consumption puzzle and how Modigliani and Friedman's theories resolve it. Question 2 delves into the Fisher model, analyzing Sara's intertemporal budget constraint, calculating the interest rate, and examining how changes in the interest rate affect consumption. Question 3 explores the Fisher's model with a utility function. Question 4 focuses on the IS-LM model, exploring shifts in the investment demand function and the relationship between the marginal product of capital, rental rates, and investment. Finally, questions 5 and 6 examine the relationship between interest rates and investment, and Tobin's Q, including its components and implications. The solution provides detailed explanations and calculations to aid in understanding these economic principles.

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

rental firm will reduce its capital holdings. However, as it reduces those capital holding, the real
rental rate will rise, as reduced capital raises the MPK. One way to think about all of this is to
define the net investment function (In (·)), where net investment is simply the change in the total
amount of capital: ∆).
Q5. a)
http://www.economicsdiscussion.net/is-lm-curve-model/algebraic-analysis-of-is-lm-model-with-
numerical-problems/10609
If the interest rate results to more investment, thus investment is negatively linked to the interest
rate.
b.) An increase in labor results in a reduction on investment. Since an increase in labor results to
high wages, thereby reducing the return to investment.

https://www.economicsonline.co.uk/Competitive_markets/The_labour_market.html
Q6). Tobin Q
a). Tobin’s q is the proportion between the market value of a physical asset and its value of
replacement. Nicholas Kaldor first initialized Tobin Q in the year 1966 in his article Macro
Economic Theories of Distribution and Marginal Productivity.
b). Tobin Q = Total market value of the firm
Total asset value of the firm
ci). Replacement value
ii). Market value
iii). Intrinsic value