Consider a competitive market served by many domestic and foreign firms. The domestic demand for thse firms' product is \(Q^{4} = 500 -1.5P\) The supply function of the domestic furms is \(Q^{SD} = 50 + 0.5P\) while that of foreign firms is \(Q^{SF} = 250\)

a. Determine the equilibrium price and quantity under free trade.

b. Determine the equilibrium price and quantity when foreign firms are constrained by a 100-unit quota.

c. Are domestic consumers better or worse off as a result of the quota?

d. Are domestic producers better or worse off as a result of the quota?