A find the marshallian demands of x for both types of

Question

Assume that there are two types of consumers. In particular, consumers of type 1 has utility function u(x, y) = x^0.5 y^0.5, whereas consumer of type 2 has u(x, y) = x^0.3 y^0.7. Both of them have income given by I>0, and the prices denoted are by P_X and P_Y, as usual.

a) Find the Marshallian demands of x for both types of consumers.

b) In what follows, suppose that there are 50 consumers of type 1 and 100 of type 2. Find the market demand of x. Does the price of y affect this demand?

c) Now suppose that I= 2 and that the market supply of X is given by Q_S = 55 + 55P_X. Compute the short-run equilibrium price and its corresponding quantity.