NUMERICAL PROBLEMS ON CLASSICAL AND KEYNESIAN ECONOMICS Basic Information: ππΆ o πππ = o πππ = o πππ + πππ = 1 o πππ = o πππ = o πππ + πππ = 1 o πΌππ£ππ π‘ππππ‘ ππ’ππ‘ππππππ (πΎ) = o ππ = πΎ β ππΌ = ( o At equilibrium, income = expenditure ππ ππ ππ πΆ π π π 1 1βπππ 1 1βπππ ) β ππΌ = ( 1 πππ Here, S stands for saving C stands for consumption I stands for investment Y stands for income mpc stands for marginal propensity to consume mps stands for marginal propensity to save apc stands for average propensity to consume aps stands for average propensity to save = 1 πππ ) β ππΌ = ππ ππΌ 1. If mpc is 0.75, calculate the value of mps and investment multiplier. Solution: given mpc= 0.75 mps = 1- mpc= 1- 0.75 = 0.25 πΌππ£ππ π‘ππππ‘ ππ’ππ‘ππππππ = 1 1βπππ = 1 1 β 0.75 = 1 1 β 0.75 =4 2. If value of multiplier is 5, calculate mpc. Solution: given, investment multiplier (K)= 5 We have, πΎ = 1 1βπππ ππ , 5 = 1 1 β πππ ππ, πππ = 0.8 3. In an economy, investment increases by Rs 200 crores. As a result of it, total income increases by Rs. 1000 crores. Calculate mpc. Given, πππππππ π ππ πππ£ππ π‘ππππ‘ = ππΌ = 200ππππππ ππππππ π ππ ππππππ = ππ = 1000ππππππ We have, πΌππ£ππ π‘ππππ‘ ππ’ππ‘ππππππ = ππ, ππ, ππ, ππ ππΌ 1 ππ = 1 β πππ ππΌ 1 1000 = 1 β πππ 200 1 1000 = 1 β πππ 200 πππ = 0.8 4. In an economy, investment increases from Rs 300 crores to 500 crores As a result of it, total income increases from Rs. 1000 to Rs. 2000 crores. Calculate value of investment multiplier and mps. Given, initial investment (I1) = Rs 300 crores Final investment (I2) = Rs 500 crores Increase in investment = I2 β I1= dI= 200 crores initial income (Y1) = Rs 1000 crores Final investment (Y2) = Rs 2000 crores Increase in investment = Y2 β Y1= dY =1000 crores ππΌ = 200ππππππ We have, πΌππ£ππ π‘ππππ‘ ππ’ππ‘ππππππ (πΎ) = πΉππ’π‘βππ, πΎ = ππ 1000 = ππΌ 500 1 ππ = πππ ππΌ ππ, 1 1000 = πππ 200 ππ, 1 1000 = πππ 200 πππ = 0.2 5. In an economy, mpc = 0.75. In this economy what will be the effect on total income if investment increases by Rs 300. Given, mpc = 0.75 Increase in investment= dI Increase in income =dY? 1 We have, ππ = ( ) β ππΌ 1βπππ 1 ππ = ( ) β 300 1 β 0.75 ππ = 1200 ππππππ 6. Suppose you have the following information about a closed economy: C = 50 + 0.80 Y I =200 G = 100 Where C is consumption, I is investment, G is Government expenditure and Y is income. a) Find out the equilibrium level of income. b) Suppose G increases to 125 what is the new equilibrium level of income? c) What level of G is needed to achieve a target income of 2000? a) At equilibrium, Income = Expenditure i.e. Y = C + I + G or, Y = 50 + 0.80 Y + 200 + 100 or, Y (1 β 0.80) = 350 Y= 1750 which is the equilibrium level of income. b) When G increases to 125 At equilibrium, Income = Expenditure i.e. Y = C + I + G or, Y = 50 + 0.80 Y + 200 + 125 or, Y (1 β 0.80) = 375 or, Y = I 875 which is the new equilibrium level of income when G increases to 125 c) To achieve a target income of 2000, G=? At equilibrium, income = expenditure Y=C+I+G or, 2000 = 50 + 0.80 *2000 + 200 + G or, G = 2000 β50 β 1600 β 200 or, G= 150 Hence government expenditure should be 150 to achieve income target of Rs. 150 6. Suppose that the economy is characterized by the following structural Equations: C = 160 + 0.6 (Y βT) I =150; G = 150; T = 100. Where C is consumption, I is investment, G is Government expenditure, T is income tax and Y is income or output. a) Determine the equilibrium output level. b) If G rises to 200, what is the how equilibrium level of output? What is the Value of the govt. expenditure multiplier? Interpret the results. c) If tax falls to 50, by how much will equilibrium output rise? What is the value of tax multiplier? Solution: a) At equilibrium, output (income) = Expenditure i.e. Y = C + I + G or, Y = 160 + 0.6 (Y β 100) + 150 + 150 Y (1 β 0.6) = 460 β 60 Y = 1000 which is the equilibrium level of output b) When G increases to 200 At equilibrium, output = expenditure Y=C+I+G or, Y = 160 + 0.6 (Y β 100) + 150 + 200 Y (1 β 0.6) = 510 β 60 Y = 1125 which is the new equilibrium output when G increases to 200 Now, increase in G = dG = 200 - 150 Increase in output Y = dY = 1125- 1000 = 125 πΊππ£πππππππ‘ ππ₯ππππππ‘π’ππ ππ’ππ‘ππππππ = ππ ππΊ = 125 50 = 2.5 Hence with an increase in government expenditure, real output increases. Output increases by 2.5 times of increase in government expenditure. c) When T falls to 50 At equilibrium, output = expenditure i.e. Y = C + I + G or, Y = 160 + 0.6 (Y β 50) + 150 + 150 or, Y (1 β 0.6) = 460 β 30 or, Y = 1075 which is the new equilibrium output when T falls to 50 Hence due to fall in tax to 50, real output will increase to 1075 Now, decrease in T = dT= 100 β 50 = 50 Increase in output Y = dY = 1075 β 1000 = 125 π‘ππ₯ ππ’ππ‘ππππππ = 75 50 = 1.5 Hence with a decrease in tax, real output increases. Real output increases by 1.5 times of decrease in tax.
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