Economicsts frequenly use linear models as approximations fpr more complicated models. In Keynesian macroeconomics theory, total consumption expendiure on goods and services, C, is assumed to be a linear functions of national income, I. The table gives the values of C, and I for 1990 and 1997 in the united states.
year 1990 1997
total consumption (c) - 3839 - 5494
National Income (I) - 6650 - 4215
a. Find the formula for C as a function of I.
b. The slope of the linear function is called the marginal propensity to consume. What is the marginal propensity to consume for the United State from 1990- 1997 ?
Please recheck your numbers. The 4215 doesn't look right. It implies that consumption increased while income dropped in 1997. The number 9215 would fit a linear model much better than 4215.
those are the numbers on my paper
Check your numbers. You have total consumption rising from 90 to 97, while national income is falling
To find the formula for C as a function of I, we can use the two given points (C, I) and the formula for a linear function, y = mx + b.
Using the points (3839, 6650) and (5494, 4215), we can find the equation of the line:
First, calculate the slope, m:
m = (I2 - I1) / (C2 - C1)
= (4215 - 6650) / (5494 - 3839)
= -2435 / 1655
≈ -1.471
Now, let's substitute one of the points into the equation y = mx + b and solve for b:
6650 = (-1.471)(3839) + b
b = 6650 + 1.471(3839)
b ≈ 6650 + 5643
b ≈ 12293
Therefore, the equation for C as a function of I is given by:
C = -1.471I + 12293
To find the marginal propensity to consume (MPC) for the United States from 1990-1997, we need to determine the slope of the linear function, which is the coefficient of I in the equation.
From the equation C = -1.471I + 12293, we can see that the coefficient of I is -1.471. This value represents the MPC.
Thus, the marginal propensity to consume for the United States from 1990-1997 is approximately -1.471.