Keynes Postulated That the Marginal Propensity to Consume $\left( \mathrm { MPC } = \frac { \Delta C } { \Delta Y _ { p d } } \right)$

Essay

Keynes postulated that the marginal propensity to consume $\left( \mathrm { MPC } = \frac { \Delta C } { \Delta Y _ { p d } } \right)$ is between zero and one. He also hypothesized that the average propensity to consume (APC $= \frac { C } { Y _ { p d } }$ ) would fall as personal disposable income $Y _ { p d }$ increased. (a)Specify a linear consumption function.Show that the assumption of a falling APC
implies the presence of a positive intercept.