Skip to content

04 PPF

Production function

Function that defines output as a function of input(s)

\(y = f_1(l, k), x = f_2(l, k)\)

Marginal Productivity

  • \(\text{MP}_l^y = \frac{\partial y}{\partial l}\)
  • \(\text{MP}_k^{y} = \frac{\partial y}{\partial k}\)

Law of Diminishing Marginal Productivity

states that: With increase in input

  • total productivity increases
  • marginal productivity decreases

Graph

  • y = MP
  • x = input (l,k)

The graph will be a straight line with a downward slope

Production Possibility Frontier

deals with the production capacity of an economy

  • analyzes available resources
  • predicts what can be produced with those resources, with the assumption that time and technology are constant
  • analyzes various output mixes (combinations of different commodities)

Production Possibility curve

Curve that shows the optimal level of production for different combinations of commodities

what is the maximum output that can be produced of various commodities

Graph

  • \(y =\) commodity 2
  • \(x =\) commodity 1

The graph will be a curve

MRT

Marginal rate of transformation

Slope shows the real/opportunity cost of \(x\) (how much we're sacrificing \(y\)) MRT of producing \(x\) wrt \(y\) shows no of units of \(y\) to be sacrificed to increase the output of \(x\) by one unit

\[ \begin{aligned} y &= f(x) \\ \text{MRT}_{x,y} &= -\frac{\mathrm{d} y}{\mathrm{d} x} \end{aligned} \]

When we go from left to right, the slope increases from left to right, ie, cost of production of \(x\) increases

  • \(\text{MP}_k^y, \text{MP}_l^y\) increases
  • \(\text{MP}_k^x, \text{MP}_l^x\) decreases

Example: if mango’s MP is 2 and apple’s MP is 4, then 4 units of apples are to be sacrificed to produce 2 units of mangoes

\[ \begin{aligned} x &= l \cdot MP_l + k \cdot MP_k \\ \mathrm{d} y &= \mathrm{d} l_{y}(MP_l^y) + \mathrm{d} k_y(MP_k^y) \\ \mathrm{d} x &= \mathrm{d} l_{x}(MP_l^x) + \mathrm{d} k_x(MP_k^x) \\ \frac{\mathrm{d} y}{\mathrm{d} x} &= \frac{MP_k^y}{MP_k^x} = \frac{MP_l^y}{MP_l^x} \end{aligned} \]

Points on the curve

  • inside are inefficient input mix - wasting profit
  • on the curve are optimal input mix
  • outside is impossible input mix

Shift of PPC

It depends on type of technological change that occurs

also depends on change in the quantity and productivity of labor and capital

Technological change

Capital-intensive

increases productivity of capital more than productivity of labor

motivates producers to increase machines rather than increasing labor

Curve expands just for capital-intensive good side

Labor-intensive

increases productivity of labor more than productivity of capital

motivates producers to increase labor rather than increasing machines

Curve expands just for labor-intensive good side

Neutral

increases productivity of labor and productivity of capital

does not change the proportion in which labor and capital are used

causes parallel shift (equal increase/decrease)

Efficient output mix

optimal points on the curve

it is impossible to increase the output of one commodity without sacrificing the output of another

shows efficient performance

developed economies

Inefficient output mix

points inside the curve

it is possible to increase the output of one commodity without decreasing the output of another

shows underperformance

Developing economies

Unattainable output mix

points outside the curve

it is not possible to reach that output, even by using all resources

that level of output may be achieved in the future with the help of development, but not with the current resources

IDK

Proportional ratio = \(\frac{\text{capital}}{\text{labor}}\) Greater the ratio, higher the productivity of the country

circular model is more sustainable

Last Updated: 2023-01-25 ; Contributors: AhmedThahir

Comments