The rate of change of the price of a commodity with respect to time, dp /dt, in a perfectly
competitive market is equal to the product of the excess demand for the commodity and
a positive constant (alpha). The excess demand for the commodity is a function of the current
market price p of the commodity and can be calculated using the formula β1 + β2P
where β1 and β2 are constants.
Which of the following is a sufficient condition for the existence of a positive equilibrium
price in the market?
a)β1 =0 and β2 =0
b) β1 =0 and β2 <0
c) β1 >0 and β2 >0
d)none
Which of the following is a necessary condition for the existence of a positive
equilibrium price in the market?
a) β1 =0 and β2 =0
b) β1 <0 and β2 >0
c) β1 >0 and β2 >0
d)none
Which of the following is a sufficient condition for the existence of a unique and positive
equilibrium price in the market?
a) β1 =0 and β2 =0
b) β1 <0 and β2 >0
c) β1 >0 and β2 >0
d)none
Assuming that a1 > 0, which of the following is a necessary condition for the existence
of a unique and positive equilibrium price in the market?
(a) β1 =0
b) β1 <0
c) β1 >0
d) A unique positive equilibrium price cannot exist with β1 >0
equilibrium is defined to be globally stable if and only if, given any initial price for
the commodity, the commodity price converges over time to the equilibrium value.
Which of the following is a necessary condition for the existence of a globally stable
equilibrium at a positive price in the market?
a) β2 =0
b) β2 <0
c) β1 =0
d)β1 =0