please decide true of false of the statements and also give the
explain:
if the demand and supply functions for a good as follows:
Q(D)= 900-60p and Q(S)=-200+50P
statement1: the equilibrium price is $12 while the equilibrium
quantity is 300.
statement 2: if the supply is constant, but an increase in income
cause customers to be willing and able to buy 220 more units at each
price than previously, the new equilibrium price will be $12 and the
new equilibrium quantity will be 400. Doctoral Program, Managerial Economics & Decision Sciences Department::
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Statement 1. Q(D) describes the demand for the product at a given
price. Q(S) describes the supply of the product at that price.
The demand and supply are in equilibrium if the demand equals the
supply:
Q(D) = Q(S)
900-60 P = -200 + 50 P
1100 = 110 P
P = 10
Hence, the equilibrium price is 10, and not 12 (so statement one is
false).
On the other hand, the equilibrium quantity is now:
Q(D)=Q(S)= 900-60P = 900-600 = 300
Thus, the equilibrium quantity is indeed 300.
Statement 2:
Now we have
Q(D) = 900-60P + 220
= 1120-60P
To find the equilibrium, we set:
Q(D)=Q(S)
1120-60P = -200+50P
1320 = 110 P
P=1320/110 = 132/11 = 12
The new equilibrium quantity is:
Q(S) = 1120-60*12
= 1120-720
=400
So that statement two is true.
----------------
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