2. The demand function for a rm's product is P 690-\") =50 10 The rm's cost of production is C(Q) = Q3 2002 + 1250 The rm's problem is to choose the value of Q that maximizes its prot. You may occasion- ally nd an irrational number and in those cases simplify your answer as much as possible. (a) Calculate the rm's inverse demand function. (h) Calculate the rm's marginal and average cost mctions. (c) Over what range of Q does the rm have economies of scale? Over what range of Q does it have diseconomies of scale? What is the rm's lowest possible average cost of production? (d) Calculate the rm's prot-maximizing price and quantity. Justify your answer care- illy. (e) Calculate the rm's maximized prot, and the revenue and cost that produce that prot. (f) Calculate the elasticity of demand at the prot-maJdmizing point. (g) What is the rm's markup at the prot-maximizing point? Conrm that this markup has the expected relationship to the elasticity of demand calculated in part (f). (h) Calculate the price(s) that would cause the rm to break even, meaning: earn exactly zero prot