Question

Suppose the demand curve in a city is given by P = 100 - 2Q, where P denotes price and Q the local GDP. The supply curve is given by P = 10 + Q. Now Suppose that due to an initial impulse of ΔX = 10 (Increase in exports) and further induced increases in local incomes the new induced demand curve changes to P = 150 - 2Q.

Where are the local GDP and the corresponding income multiplier if prices were constantly at P = 40?

A) q = 35, income multiplier = 3.5

B) q = 55, income multiplier = 2.5

A) q = 70, income multiplier = 2.5

A) q = 95, income multiplier = 9.5

A) None of the above

Answer 1

Ans.

Correct Option is = Q = 55 and income multiplier = 2.5

Explanation -

For equilibrium,

Because Q is the local GDP , where , P = 100 - 2Q   , demand function will be Q = 50 - 1/2 P or Q = 50 - 0.5 P

and for supply where P = 10 + Q , supply function wll be Q = -10 + P

Demand function = supply function

50 - 0.5 P = -10 + P

50 - 1.5 P = - 10

1.5P = 60

P = 60 / 1.5 = 40

By putting the P values in Demand we will get the Q value ,

Q = 50 - 0.5 x 40

Q = 30

New Demand Function ,

P = 150 - 2Q

by putting the given P = 40 constant value,

40 = 150 - 2Q

Q = 110/2 = 55

So , Q will be 55

increase in exports = 10 units ,

New Q value - Old Q value , 55 - 30 = 25 units

Increase in output because of change in net exports in terms of units is 25.

So,

Increase in Local GDP (increase in output) = income multiplier x increase exports

income Multplier = 25 / 10 = 2.5

So , the income multiplier will be 2.5 at P = 40.

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