$2.$ The cost of producing machine learning software depends on an individual$$s skill. In particular, if an individual is skilled, then his or her variable cost is cS$($q$)=12$ q$2$ and marginal cost c$$ S$($q$)=$ q$.$ In contrast, if the individual is unskilled, then his or her variable cost function is cU $($q$)=2$q$2$ and marginal cost function c$$ U $($q$)=4$q$.$ In addition, suppose that machine learning is highly specialized: skill in this specific industry does not translate well to other industries. Therefore, both skilled and unskilled individuals have the same fixed cost to enter the industry, f $=12.$ Therefore, the total cost function of a skilled individual is c$$S$($q$)=12+12$ q$2,$ while the total cost function of an unskilled individual is c$$U $($q$)=12+2$q$2.($a$)$ What is the average cost function of a skilled individual? What is the average cost function of an unskilled individual? $($Hint: Average cost is total cost divided by the output.$)($b$)$ What is the minimum efficient scale for a skilled individual? What is the minimum efficient scale for an unskilled individual? $($Hint: At the minimum efficient scale, average cost and marginal cost are equal$).($c$)$ What is the lowest price, pS$,$ at which a skilled individual would enter? What is the lowest price, pU $,$ at which an unskilled individual would enter? $($Hint: average cost is as small as possible at the minimum efficient scale.$)($d$)$ Assume that there is a large $($infinite$)$ number of individuals of each skill level. What quantity does the industry supply in the long$-$run if p $>$ min$\{$pS$,$ pU $\}?$ What quantity does the industry supply in the long$-$run if p $<$ min$\{$pS$,$ pU $\}?$ Assuming that demand is positive and finite at all prices, what is the long$-$run equilibrium price? $($e$)$ Does the unskilled individual choose to enter the machine learning industry in the long$-$run equilibrium? What about the skilled individual? Explain your answer in a sentence. Now suppose that over time, $$adjacent$$ industries arise$$artificial intelligence, algorithmic trading, etc. Unskilled individuals are not affected by the emergence of these industries, but these industries offer skilled individuals additional opportunities. Consequently, a skilled individual$$s fixed cost of entering the machine learning software industry increases to $92.$ With this change, the skilled individual$$s total cost function in the machine learning industry is c$$S$($q$)=92+12$ q$2,$ and his or her marginal cost is c$$ S$($q$)=$ q$.$ All subsequent parts of the problem are about the machine learning industry after the emergence of the adjacent industries. $($f$)$ What is the average cost function of a skilled individual? $($g$)$ What is the minimum efficient scale for a skilled individual? $($h$)$ What is the lowest price, p$$ S$,$ at which a skilled individual would enter? $($i$)$ Assume that there is a large $($infinite$)$ number of individuals of each skill level. What quantity does the industry supply in the long$-$run if p $>$ min$\{$p$$ S$,$ pU $\}?$ What quantity does it supply in the long$-$run if p $<$ min$\{$p$$ S$,$ pU $\}?$ Assuming that demand is positive and finite$)$at all prices, what is the long$-$run equilibrium price? $($Hint: remember, the unskilled individual$$s technology is unaffected by the emergence of the adjacent industries: pU is the same as in part $($c$)).($j$)$ Does the unskilled individual choose to enter the machine learning industry in the long$-$run equilibrium? Does the skilled individual choose to enter the original industry in the long$-$run equilibrium? Does your answer seem weird? Explain in a sentence or two.