Eco 300. Intermediate Microeconomics Homework 4

Eco 300. Intermediate MicroeconomicsHomework 41. A rm total cost curve is given by T C (q ) = q (q 4)2 + 2q .sa) What is the formula for its AC curve?b) Marginal costs are given by M C (q ) = 3q 2 16q + 18. Graph thistogether with the AC curve.2. Trapper Joe, the fur trader, has found that his production function inpacquiring pelts is given by q = 2 H where q =the number of pelts acquiredin a day, and H =the number of hours Joe employees spend hunting andstrapping in one day. Joe pays his employees $8 an hour.a) Calculate Joe total and average cost curves (as a function of q).sb) What is Joe total cost for the day if he acquires four pelts? Sixspelts? Eight pelts? What is Joe average cost per pelt for the day if hesacquires four pelts? Six pelts? Eight pelts?c) Graph the cost curves from part a and indicate the points from partb.3. Suppose that a rm faces a demand curve that has a constant elasticityof 2. This demand curve is given by q = 256=P 2 . Suppose also that therm has a marginal cost curve of the form M C = 0:001q .a) Graph these demand and marginal cost curves.b) Calculate the marginal revenue curve associated with the demandcurve; graph the curve.c) At what output level does marginal revenue equal marginal cost?4. Assume that a rm acts as a price taker. Regardless of the demand,it sells each unit of its product for $5.a) Assume that the rm marginal cost is given by M C = 0:2q + 3.sWhat is the level of output q that maximizes prot?b) Assume the total cost is given by T C = 0:1q 2 + 3q + 10. Calculatethe rm prot.sc) Graph these results and label rm supply curve.s5. Suppose that a rm faces the demand curve of the form q = 60 2p.a) Write down the total revenue curve as a function of q .b) Assume M C = 0:2q and M R = 30 q . What output level should therm produce to maximize prots?c) Graph the demand, M C , and M R curves and the point of protmaximization.1