Consider a perfectly competitive market described by the supply function P=10+0.3Q and demand function P=60-0.2Q. If the government intervenes in the market and imposes a price restriction of P=$25, the result rounded to the nearest unit will be a:

In a perfectly competitive market, the equilibrium price is determined where the supply and demand functions intersect. To find this equilibrium, we set the supply equation equal to the demand equation.

From the supply function, we have:

[ P = 10 + 0.3Q ]

From the demand function, we have:

[ P = 60 - 0.2Q ]

Setting these equal to each other to find the equilibrium:

[ 10 + 0.3Q = 60 - 0.2Q ]

To solve for Q, we first move all terms involving Q to one side:

[ 0.3Q + 0.2Q = 60 - 10 ]

[ 0.5Q = 50 ]

[ Q = 100 ]

Now, we substitute Q back into either the supply or demand equation to find the equilibrium price (P):

Using the demand function:

[ P = 60 - 0.2(100) = 60 - 20 = 40 ]

Thus, the equilibrium price is $40 with an equilibrium quantity of 100 units.

Now, with a government-imposed price restriction of $25, we must analyze the situation with respect to