Find the price at which profit would be mximised

 1.The slope of the production possibility curve is the

A. Marginal rate of exchange

B.Margial rate of substitution

C. Average rate of transformation

D. Marginal rate of transformation ✓

Ans: D 

2.  

Solution :

5Q2+20Q+20

MC= ∆C/∆Q

5×2Q+20

MC=10Q+20......(1)

P=100-3Q.....(2)

TR=PQ

TR=(100-3Q)Q  {P=100-3Q}

TR= 100Q-3Q×Q

MR= 100-6Q ....(3)

MC=MR

10Q+20100-6Q

10Q+6Q=100-20

16Q=80

Q=80/16

Q=5

From (2). P=100-3Q

P=100-3(5)

P=100-15

P=85

Derivation of Keynes Multiplier

MPC= Marginal propensity to consume

MPS= Marginal propensity to save

I= investment

∆I= Changed Investment

S= Saving

∆S=Changed Saving

K= Keynes Multiplier

C= Consumption

Y=Income

MPC+MPS=1

MPS=1-MPC---(1)

K= 1/1-MPC or

K= 1/MPS----- ( From-- 1)

∆Y= K.∆I ( K = Keynes Multiplier)

K∆I= ∆Y

K= ∆Y/∆I

S=Y-C

Saving = Income - Consumption

∆S=∆Y - ∆C ---(2)

∆S=∆I---- (3)

K= ∆Y/∆I

K= ∆Y/∆S ----(from 3)

K=∆Y/(∆Y - ∆C) -----( from  2)

Dividing on Numerator and Denominator by ∆Y

K= (∆Y/∆Y)÷(∆Y - ∆C)/∆Y

K= 1÷(∆Y/∆Y -∆C/∆Y)

K= 1÷(1 - ∆C/∆Y)

  K =1/1-MPC. -----  ( ∆C/∆Y=MPC)

K= 1/MPS -------- ( 1-MPC= MPS)