Microeconomic

onsider a customer (i) with a utility function u(x,y)=200x25x2+y where the price of good is $p, and the price of the composite good y is one dollar ( $1). Also, assume that each onsumer has an income I. (MUx=20050x, and MUy=1) (a) Derive the consumer's demand function for goodx. Now, consider an economy with 100 exact same type of consumers. (b) Calculate an aggregate demand for only good x. Now, consider a firm which produces good x. This firm's total cost function is TC(q)=256+16q+q2 and MC(q)=16+2q (c) Calculate the Short-run supply function for this firm. Now, Consider an industry with 12 firms of this type. None of the firms is big enough to affect the price. (d) Calculate the Short-run aggregate industry supply function for good x. (e) Calculate the market equilibrium price and quantity for good x in the equilibrium. (f) Calculate each firm's profit in the short- equilibrium 2