Macroeconomics 2

Posted: August 25th, 2021

Student’s Name

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Macroeconomics 2

Question 1

Q1 -1. The plot of Three Components Of GDP: Consumption, Investment and Net Exports for US Economy, 1978-2018

Data source:Group, World B: World Development Indicators

From figure 1 above, it can be shown that gross investment in expenditure gradually increased over the years, unlike consumption expenditure which exhibits fluctuations particularly between 1995 to 2000. Subsequently, net export for the U.S has exhibited stable and constant increase over the years.

Q1-2. Langrangian Equation; Consumption and Leisure

False. There is no point when consumption, c = w (1 – l). Expenditure on consumption increase with an increase in leisure, hence the equation would be, c = w(1+l), where l refers to leisure time.

Q1-3. Relationship Between Household Consumption and Interest Rate, R

True. Based on the equation; , it implies that:

Hence, C1 and r are inversely related such that an increase in r leads to a decrease in consumption, c1.

Q 1-4. Relationship Between Household Consumption, C1 & C2 and Period Income, Y2

False. Given that
 and that  it implies that an increase in period 2 income leads to an increase in consumption both in periods 1 and 2.

Question 2

Q2-1.  Profit Output

Profit is a net outcome of total revenue generated by the firm less the total costs incurred in production.

 Hence;

Firms production technology = at time t

The total cost of labor at time t = Nt *wt

Profit function would be;

Q2-2.  Production Function Has Constant Returns to Scale

Returns to scale is a measure of how much any additional output can be achieved following a proportional change in the production factors (Hayashi 89). Hence, returns to scale are constant when the constituent factors sum up to one (1) that is, the sum of α + (1- α) = 1. This implies that a positive change in the input factors by a positive proportion results in a similar proportional change in the output (Friedman 107). Hence given the production function as; , the exponents α and (1- α) for K and N factors, when summed up yields 1, which closely relates to the production function’s constant to scale properties. If K and N are increased by a similar positive value, let’s say v > 0, output  increases with the same positive value, Y as shown below;

) for any v > 0

)

=

= vY, hence changes in K and N by value v at time t is constant, Y.

Q2-3.

Given K1, the firm’s problem is to choose N1, N1, and K2 to maximize , the optimal condition can be derived as:

Objective, Maximize ,

Subject to the cost of production factors;

,

Kt >0, Nt >0

By the lagrangian equation; l =  – λ ()

First-order conditions:

•  2+r = 0

•  α= 0

•  (1-α)= 0

Given t = 2, the optimal condition for Kt and Nt at t=2 will be;

•  α= 0,

•  (1-α)= 0

Q2-4. Effects of Changes in A and R on Investment

Capital accumulation,  and given the real interest rate as r >0 at time t where 0 < σ < 1 for a perfectly competitive market, effects of changes in A and r can be illustrated as;

Return on investment = Capital accumulation X interest rate = I_t=1 *r

= *r, A is total factor productivity hence, net revenue will be:

= *r – A*(

Change in A effect;

Therefore, A has a negative effect on investment such that a unit increase in A contributes to a unit decrease in investment.

Change in r effect;

Hence, r has a positive effect on investment such that a unit increase in r leads to a unit increase in the level of investment.

Works Cited

Friedman, Milton. A Theory of the Consumption Function. San Francisco: Golden Springs Publishing, 2016. Print.

Group, World B. World Development Indicators 2011. Washington: World Bank, 2011. Print.

Hayashi, Fumio. Understanding saving: evidence from the United States and Japan. Cambridge, Mass: MIT Press, 1997. Print.