Consider an economy with k=2 identical price-taking firms producing lettuce, each maximizing profits according to some cost function, c(yk)=yk2 Suppose prices are set according to some (exogenous) inverse market demand function, p(YD)=aYD where a>0 is some exogenous demand parameter. (a) Set up the firm's profit maximization problem. (b) Derive each firm's output supply function for lettuce, yk(p). Is it upward-sloping in price? (c) Derive the market supply function for lettuce, YS(p). (d) What is the partial equilibrium price, p ? (e) What is the total equilibrium quantity of lettuce? (f) Now suppose there is instead a single price-setting firm. What is its profit maximization under price setting? How does it differ from the one in (a)? Without solving, how would you expect price-setting behavior to affect the equilibrium price, relative to the one in (d)? Explain. Consider an economy with k=2 identical price-taking firms producing lettuce, each maximizing profits according to some cost function, c(yk)=yk2 Suppose prices are set according to some (exogenous) inverse market demand function, p(YD)=aYD where a>0 is some exogenous demand parameter. (a) Set up the firm's profit maximization problem. (b) Derive each firm's output supply function for lettuce, yk(p). Is it upward-sloping in price? (c) Derive the market supply function for lettuce, YS(p). (d) What is the partial equilibrium price, p ? (e) What is the total equilibrium quantity of lettuce? (f) Now suppose there is instead a single price-setting firm. What is its profit maximization under price setting? How does it differ from the one in (a)? Without solving, how would you expect price-setting behavior to affect the equilibrium price, relative to the one in (d)? Explain