midterm question

2 Long questions 1. Consider a farmer who produces cabbages using tractors and labor inputs. Cabbages are produced using the production function given by Q = $1 12", where Q is output, x] is labor input and z, is tractor input. a) Define the farmer's long-run profit maximization problem. b) It takes three months for new tractors to arrive while labor inputs can be changed within a day. Define and solve the profit maximization problem of the farmer for the next month if he has 4 tractors. Assume that each tractor cost nothing due to a government subsidy programme, while each unit of labor costs 5 TL and each unit of cabbage can be sold for 10 TL. c) How much profit does the farmer make? d) Show the short-run equilibrium for the amount of labor inputs on the same graph by drawing a representative production function and isoprofit curve. Write down the slope of the isoprofit line