Calculate the equilibrium quantity of rice consumed in japan

Question

Problem 1: Tariffs

Rice is traded in a competitive world market.  At the world price of $0.10 per pound, unlimited amounts of rice can be imported into Japan for purchase in the Japanese rice market.  (e.g.  There is an infinite supply of rice at the world price of $0.10 per pound.)

The domestic demand and supply of rice in Japan is given by:

Japanese domestic rice demand: Q^d(p) = 34 - 100 . p
Japanese domestic rice supply: Q^s(p) = -2 + 50 . p

Quantity is measured in millions of pounds of rice, and the price is given in dollars per pound.

A) Calculate the equilibrium quantity of rice consumed in Japan at the world price of $0.10 per pound, and indicate the quantity of rice imports at the world price.  Sketch a graph to illustrate the Japanese rice market under free trade, clearly labeling the effective supply curve in the Japanese market and the level of imports.

B) Calculate the new equilibrium price and quantity of rice in Japan, and indicate the level of domestic rice production. Once again, sketch a graph of the Japanese rice market to illustrate the effect of a rice import quota of 6 million pounds.

C) Calculate the change in consumer surplus caused by imposing the rice import quota of six million pounds.  The consumer surplus formula is given below:

Consumer surplus: CS = 1/2 x [p(Q^d = 0) - p(Q^d = Q^*)] x Q^*
Consumer surplus: CS = 1/2 x [$0.34 - p(Q^d = Q^*)] x Q^*

If the Japanese government would have decided to use a tariff to limit rice imports to 6 million pounds, would there have been any differential welfare effect?  Describe.