I need help solving problem 4 sections a-d. Please note that this is not graded work. I obtained this question from an old text book to help me practice problem sets. Do let me know if you have additional questions. 4. Shutdown price. Consider a firm that washes cars and has a cost functionC(q) = 2q² +7q+10,where q denotes the number of cars washed. Intuitively, the first two terms capture the firm's vari-able cost, because they depend on the output the firm produces, whereas the last term representsits fixed cost, because it is not a function of output q.(a) Find the firm's marginal cost curve, its average cost curve, its average variable cost curve, andits average fixed cost curve.(b) Assume that the firm operates in a perfectly competitive industry, taking a príce of p= $18 asgiven. Which output level does the firm choose in this scenario?(c) What if the price of output decreases to p= $11?(d) For which price will the firm choose to shut down its operations?

MC(Marginal cost) refers to the extra/additional cost that the firm has to incur in order to produce an extra/additional unit of output(Q). AC(average cost) in the production is the per unit cost which is obtained by dividing overall cost(TC) by output(Q). AVC(average variable cost) is the per unit total VC(variable cost). It is obtained by diving overall VC by output(Q). AFC(average fixed cost) is the per unit FC(fixed cost). It is obtained by dividing overall FC by output(Q). Given - C(q) =12q2+7q+10VC =12q2+7qFC = 10 Here, q is the number of cars washed. a) MC= ∂TC∂qMC =∂(12q2+7q+10)∂qMC = q + 7AC =TCqAC =(12q2+7q+10)qAC = 12q+7+10qVC = 12q2+7qAVC = VCqAVC = 12q2+7qqAVC = 12q+7FC = 10AFC = FCqAFC = 10q b) In a PC (perfectly competitive) market, the competitive output is obtained at the point where P = MC. p =$18MC = q+7In PC,p = MC18 = q+7q = 11 Thus, the output(q) that the firm chooses here in PC is 11 units. c) Now, if the price of output(q) is reduced to $11, the new quantity(q*) will be - p = $11MC =q+7p = MC11 = q + 7q* = 4 Thus, the output(q) that the firm chooses at price(p) =$11 is 4 units. d) In a PC (perfectly competitive) market, firms shut down at the minimum of the AVC ( average variable cost) curve. The minimum of AVC is obtained at the point where q is 0. So, AVC = 12q + 7AVC = 7 (q = 0) so, the firm will not operate at a price(p) lower than $7 and will shut down. Hence, MC is obtained as q+7, AC = 12q + 7+10q, AVC=12q + 7 and AFC = 10q. b) At, p =$18, the output that firm produces/chooses is 11 units. c) At, p = $11, the output that firm produces/chooses is 4 units. d) The firm will shut down at price less than $7.