18:29 E 8 00000162\" I Yourtask 1. Read the questions carefully. Make sure you show the solutions along with the equations. Direct answers are not accepted, 3. Explain your answers in details. 1.The Zinger Company manufactures and sells a line of sewing machines. Demand per period (Q) for a particular model is given by the following relationship: Q = 400 - 0.5? where P is price. Total costs (including a "normal" return to the owners) of producing Q units per period are: TC = 20,000 + 500 + 302 (3) Express total profits (TL) in tErms of Q. (h) At what level of output are total profits maximized? What price will be charged? What are total profits at this output level? (c) What model of market pricing has been assumed in this problem? Justify your answer. 2. Zar Island Gas Company is the sole producer of natural gas in the remote island country of Zar. The company's operations are regulated by the State Energy Commission. The demand function for gas in Zar has been estimated as; P = 1.000 0.20 where Q is output (measured in units) and P is price (measured in dollars per unit). Zar Island's cost function is: TC = 300,000 + 10Q This total cost function does n_ot include a "normal" return on the firm's invested capital of 54 million. (a) In the absence of any government price regulation, determine Zar Island's optimal (i) output level, (ii) selling price, (iii) total prots, and (iv) rate of return on its asset base. (b) The State Energy Commission has ordered the firm to charge a price which will provide it with no more than a 12 percent return on its total assets. Determine Zar Island's (i) output level, (ii) selling price, and (iii) total profits under this constraint. Hint: The roots of the quadratic equation: b i (b2 - 4cm) ax2+bx+c=0 => x: 2a 3. Two companies (A and B) are duopolists that produce identical products. Demand for products is given by the following demand function: P = 10,000 QA QB where QA and 0.3 are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are: TCA = 500,000 + 200 Q + 0.50% TCB = 200,000 + 400 QB + 0,2, an\"..- LL\". u... a"..- no... -..;. :_..4-........1-...u.. .. :_ u... r-..__...a. ....A..| u.|....; :. -....i. 1:-.. III C) <