There are two types of firms, type A and type B, which make vape pens/e-cigs. There are 8 type A firms each with a cost function CA(y)=y+2y2, and there are 20 type B firms each with a cost function CB(y)=y2. The market demand for vape pens is given by D(p)=37p. 12. Consider a short-run market with 0 type A firms and n>0 type B firms. Derive the market supply for any given n. 13. What is the short-run equilibrium price pE(n) and quantity yE(n) as a function of the number of type B firms n ? 14. What is each individual firm's supply to the market at the given short-run equilibrium price as a function of n ? 15. Show that pE(n)>minACB for any finite positive number n. This implies that, regardless of how big n gets, each of the type B firms in the market would be making strictly positive profits. This would undoubtedly attract even more type B firms to enter making n grow larger. 16. As more and more firms enter, n goes to infinity. What does each individual firm's supply converge to as n goes to infinity? What do pE(n) and yE(n) converge to as n goes to infinity. (You do not have to prove anything here. Just use a calculator or website like Wolfram Alpha to plug in bigger and bigger values of n and see what pattern emerges). The takeaway from this last section is that type B firms can always make a profit in a short-run market. Attracted by these profits, more and more type B firms will enter the short-run market. Over time, there will be an infinite amount of firms with each firm producing a very small amount. There are two types of firms, type A and type B, which make vape pens/e-cigs. There are 8 type A firms each with a cost function CA(y)=y+2y2, and there are 20 type B firms each with a cost function CB(y)=y2. The market demand for vape pens is given by D(p)=37p. 12. Consider a short-run market with 0 type A firms and n>0 type B firms. Derive the market supply for any given n. 13. What is the short-run equilibrium price pE(n) and quantity yE(n) as a function of the number of type B firms n ? 14. What is each individual firm's supply to the market at the given short-run equilibrium price as a function of n ? 15. Show that pE(n)>minACB for any finite positive number n. This implies that, regardless of how big n gets, each of the type B firms in the market would be making strictly positive profits. This would undoubtedly attract even more type B firms to enter making n grow larger. 16. As more and more firms enter, n goes to infinity. What does each individual firm's supply converge to as n goes to infinity? What do pE(n) and yE(n) converge to as n goes to infinity. (You do not have to prove anything here. Just use a calculator or website like Wolfram Alpha to plug in bigger and bigger values of n and see what pattern emerges). The takeaway from this last section is that type B firms can always make a profit in a short-run market. Attracted by these profits, more and more type B firms will enter the short-run market. Over time, there will be an infinite amount of firms with each firm producing a very small amount
