A Keynesian Consumption Function:
In his famous 1936 book, A General Theory of Employment, Interest and Money, the noted British economist John Maynard Keynes proposed a theoretical relationship between income and personal consumption expenditures. Keynes argued that as income went up, consumption would rise by a smaller amount. This theoretical has been empirically tested many times since 1936.
Milton Friedman, former professor of economics at the University of Chicago and winner of the Nobel Prize in economics, collected extensive data on income and consumption in the United States over a long period of time. Shown below are 10 observations on annual levels of consumption and income used by Friedman in his study. Using these data, derive a consumption function under the assumption that there exists a linear relationship between consumption and income. Figures are in billions of dollars.
________________________________________________________________
Year Income Consumption ________________________________________________________________
1 284.8 191.0
2 328.4 206.3
3 345.5 216.7
4 364.6 230.0
5 364.8 236.5
6 398.0 254.4
7 419.2 266.7
8 441.1 281.4
9 447.3 290.1
10 483.7 311.2
_________________________________________________________________
Determine the dependent and independent variable and calculate a consumption factor. Establish the relationship between income and consumption and interpret. Discuss the fit of the data and explain.
To derive a consumption function using the given data, we need to establish a relationship between the dependent variable (consumption) and the independent variable (income).
In this case, income is the independent variable as it is assumed to have an impact on consumption. Consumption, on the other hand, is the dependent variable as it is expected to change based on the level of income.
To determine the consumption function, we assume a linear relationship between income and consumption. A linear relationship suggests that for a certain increase in income, consumption will increase by a constant proportion.
To calculate the consumption factor (slope), we can take any two points from the data and use the formula:
Consumption Factor = (Change in Consumption) / (Change in Income)
Let's use the first and last data points to calculate the consumption factor:
Change in Income = 483.7 - 284.8 = 198.9
Change in Consumption = 311.2 - 191.0 = 120.2
Consumption Factor = 120.2 / 198.9 = 0.604
Now that we have the consumption factor, we can establish the relationship between income and consumption:
Consumption = (Consumption Factor) * (Income)
The consumption function in this case would be:
Consumption = 0.604 * Income
Interpreting the relationship:
According to the derived consumption function, for every unit increase in income, consumption is expected to increase by 0.604 units. This implies that as income rises, consumption also increases, but at a smaller rate.
The fit of the data:
To assess the fit of the data to the consumption function, we can compare the predicted consumption values obtained from the function with the actual consumption values provided in the data set. By calculating the residuals (the differences between the predicted and actual consumption for each year), we can evaluate how closely the consumption function aligns with the data points.
Examine each year's predicted consumption by substituting the corresponding income value into the consumption function. Then calculate the residuals by subtracting the predicted consumption from the observed consumption. A smaller magnitude of residuals indicates a better fit.
By comparing the residuals calculated for each observation, we can determine whether the consumption function adequately represents the relationship between income and consumption.