The market demand for a good consists of two types of consumers, type A and type B. Each type has 2 consumers. Each type A consumer has an individual demand function given by D_A(p) = 200 - 4p and each type B consumer has an individual demand function given by D_B(p) = 100 - p, where p is the price of the good.

a. Derive the aggregate demand function for each type and the aggregate market demand function. Present graphically the aggregate market demand function. Mark the intercepts correctly.

b. Suppose that the supply function is perfectly elastic and it is given by p = $20. Find the amount purchased by each type of consumers and the equilibrium quantity. Illustrate the equilibrium quantity with a graph.

c. Now, suppose instead that the supply function is perfectly inelastic and it is given by q = 40. Find the equilibrium price. Illustrate the equilibrium price with a graph. Do both types of consumers buy the good?