Suppose savings function is S = -5 + 0.3Y, then find the correct answer from below:

Correct option is D

Correct Answer: (d) APC > MPC

Explanation: To determine the relationship between Average Propensity to Consume (APC) and Marginal Propensity to Consume (MPC), we first derive the Consumption Function from the given Savings Function.

• Given Savings Function: S = -5 + 0.3q (where q represents Income, usually denoted as Y).
  
  • Here, -5 is autonomous saving (dissaving).
  • 0.3 is the Marginal Propensity to Save (MPS) because $$MPS = \frac{dS}{dq}$$​.

• Derive Consumption Function: We know that Income (Y) = Consumption (C) + Savings (S). Therefore, C = Y - S.  
  
• Substitute the savings function:
  • C = Y - (-5 + 0.3Y)
  • C = 5 + Y - 0.3Y
  • C = 5 + 0.7Y

• Calculate MPC and APC:
  • MPC: The slope of the consumption function (dC/dY). MPC = 0.7.
  • APC: The ratio of total consumption to total income (C/Y). $$APC = \frac{5 + 0.7Y}{Y} = \frac{5}{Y} + 0.7$$.
  • Comparison:
    
    • Since income (Y) is positive, the term $$\frac{5}{Y}$$​ is a positive number.
    • Therefore, $$0.7 + \frac{5}{Y}$$​ will always be greater than 0.7.
    • Result: APC > MPC.