Question

Assuming that equilibrium GNP can be found at the intersection of the savings and investment schedules, show that equilibrium GNP can be found at the intersection of the consumption plus investment schedule and the \(45^{\circ}\) line.

Short answer

The equilibrium Gross National Product (GNP) can be found at the intersection of the consumption plus investment schedule and the 45-degree line, as well as the intersection of the savings and investment schedules. This is because, at equilibrium GNP, savings (S) equal investment (I), making the statements \(Y=C+I\) and \(Y=C+S\) equivalent. Thus, the intersection of the consumption plus investment schedule and the 45-degree line represents the same equilibrium point as the intersection of the savings and investment schedules.

Step-by-step solution

Consumption

Consumption is the total spending by households on goods and services during a specific period of time.

Investment

Investment is the spending on capital goods to be used for the production of goods and services in the future.

Savings

Savings is the portion of income not spent on consumption. It's equal to disposable income minus consumption.

45-Degree Line

The 45-degree line represents all points where the value of the x-axis is equal to the value of the y-axis. In the context of this exercise, it's where national income (GNP) is equal to consumption plus investment. #Step 2: Finding equilibrium GNP using the savings and investment schedules#

Equilibrium GNP

Equilibrium GNP is the level of GNP at which the savings and investment schedules intersect. In other words, it's the level of GNP where savings equal investment. #Step 3: Finding equilibrium GNP using the consumption plus investment schedule and the 45-degree line#

Consumption Plus Investment Schedule

The consumption plus investment schedule shows the sum of consumption and investment at each level of GDP.

Intersection with the 45-Degree Line

The equilibrium GNP is found at the intersection of the consumption plus investment schedule and the 45-degree line. At this point, GNP (Y) is equal to consumption plus investment (C+I) or: \[Y=C+I\] #Step 4: Establishing the relationship between savings, investment, and the 45-degree line#

Relationship between Savings and Investment

Since savings (S) is equal to disposable income minus consumption (Y-C), we can say that: \[S=Y-C\] But we also know that at equilibrium GNP, savings (S) equal investment (I), therefore: \[S=I\] Replacing I with S in the equation \(Y=C+I\), we get: \[Y=C+S\] #Step 5: Proving the equivalence of both methods#

Equivalence of both methods

We have established that \(Y=C+I\) is the condition for equilibrium GNP when we find the intersection of the consumption plus investment schedule and the 45-degree line, while \(Y=C+S\) is the condition for equilibrium GNP when considering the intersection of the savings and investment schedules. Since S=I at the equilibrium, both methods give the same result: \[Y=C+I\] \[Y=C+S\] Hence, we can conclude that the equilibrium GNP can be found at the intersection of the consumption plus investment schedule and the 45-degree line.

Key concepts

Consumption

Understanding consumption is crucial when analyzing an economy's equilibrium Gross National Product (GNP). Consumption represents the total expenditures by households on goods and services over a given period. It is a primary component of an economy's aggregate demand and reflects the economic well-being of the society.

When individuals receive their disposable income, they have two choices: to consume or to save. The more they spend on consumption, the less they have for savings. This spending activity drives the production of goods and services and can be influenced by several factors, including consumer confidence, interest rates, and inflation. The relationship between income and consumption is often depicted by the consumption function, which is a cornerstone in understanding macroeconomic equilibrium.

Investment

The investment component of the economy refers to the purchase of capital goods that will be used for future production. This includes spending on infrastructure, machinery, equipment, and technology. Investment is a forward-looking measure, indicative of the economy's potential for growth and expansion.

Unlike consumption, which is primarily driven by individual and household decisions, investment decisions are typically made by businesses and governments. The level of investment may fluctuate based on expected returns, interest rates, and economic forecasts. High investment levels usually signal confidence in the economy's future and can lead to increased production capacities and job creation. Investment, alongside savings, is significant in determining the equilibrium level of GNP.

Savings

The concept of savings is intertwined with consumption and investment. Savings represent the portion of disposable income that is not spent on consumption; it is essentially deferred consumption. The savings rate within an economy can impact the available funds for investment and influence the overall economic growth.

Economists analyze savings to understand consumer behavior, assess the health of an economy, and predict future consumption patterns. Savings can be private, as in the case of individuals and households, or public, in the form of government budget surpluses. A higher savings rate might suggest that consumers are more cautious about their financial future, while lower savings could indicate confidence in the economy or a higher propensity to consume.

45-Degree Line

The 45-degree line is a tool used in economics to help visualize where an economy is at equilibrium. This line represents all the points where the output, or GNP in this context, is equal to aggregate expenditure, which is the sum of consumption and investment.

Any point on this line shows that what is being produced in the economy is being purchased — there's neither excess supply (which could signal producers to cut back on output) nor excess demand (which would prompt an increase in production). The intersection of the consumption plus investment schedule with this line indicates the equilibrium GNP, where planned spending is equal to actual output—ensuring that the economy is balanced with no unplanned accumulation or decumulation of inventories.