The demand function for a good is Qa bp and the supply funct

The demand function for a good is Q-a bp, and the supply function is Qs = c + ep + ft, where a, b, c, e, and fare positive constants and t is the average temperature in a month. Show how the equilibrium quantity and price vary with temperature The effect of a change in t on the equilibrium price (p) is- dp dt

Solution

We know at equilibrium Qd=Qs

Thus a-bP=C+eP+ft

a-c-ft=(b+e)P

P=(a-c-ft)/(b+e) and Q=[a-b(a-c-ft)]/(b+e)

dP/dt=-f/(b+e) and dQ/dt=bf/(b+e)