MICROECONOMICS Problem Set 2 GI. Viyelt produces pens. using as inputs only labour {LJ and machines {K}. His production function is given by the following equation,Q= I'll-(KW-l + [L)' [a] What type of returns to scale does Viyek's production function exhibit? At the end of last year1 lin'iyelt bought his only machine for Rs. IUOO. He will use this machine for next 5 years, aer which the machine will have no value. Viyek will calculate depreciation linearly at 20% of the total value ofthe machine per year. This machine has no other use hesides lll'iyelt's production of pens, and, at this moment Viyek cannot buy any more machines. [bJ What is Vivek's annual fixed cost of production? ls the tted cost sunk or not? Explain. to] What is Vivek's demand for labour as a function of the quantity he wants to produce annually?I id) Assuming that wage equals i, What is Viy'elt's annual total cost function? Q2. Anurag is the manager ofSpeed, a retail store in Ranchi that sells high fashion athletic shoes. The shoes sold in his store are very different from what is sold in any nearby stores, which gives him market power. He maintains this market power by contpletely changing the product line every quarter. He has three options for what to do with any shoes that are left unsold at the end of the quarter. 1' He allows his three employees to buy any shoes they want at 15% of the retail price [although they are allowed to buy shoes only for their own use. not for resale}. 1' He can sell shoes to an outlet store located in Jamshedpur. willing to purchase any amount from Speed, for Rs. 200 per pair [assume that there are no additional transaction costs}. c He can give the shoes to the Red Cross who will give them away to disaster victims. Anurag buys shoes wholesale for Rs. 890 per pair. All the other costs of running the store are fixed costs. unavoidable in the short run. The weekly demand for shoes at lslictory is P = 1690 0.0625 0 where P is measured as rupees per pair of shoes. and Q is the number of pairs of shoes sold in the stone per week. i) How many pairs of shoes per week should Anurag plan to order for the stone for the upcoming quarter? At what price per pair should he plan to sell those shoes? ii) One of Anurag's employees suggests that Anurag should have a sale on shoes for the last two weeks of the quarter. Is this a good idea? If so. what price should Anurag set as a sale price for the shoes? [f you think it is not a good idea, explain why not. Q3. It's a bad day at Caparo India (henceforth, CD). The group offers end-to-end solutions in designing, developing and manufacturing automotive systems, assemblies, advanced composites, modules and components to Indian Automotive OEMs and Engineering Industry. Caparo India leverages its exhaustive capabilities in metal Stamping, Fastening, Tubing, Forging and Aluminium Foundry businesses, coupled with its state-of-the-art Tool Room and R&D Centre, to service top-notch clients such as GM, Ford, Maruti, Honda, and Tata Motors. CI agreed to produce the metal body panels for Honda's new SUV, and now Honda has scaled down its production estimates from 100,000 to 10,000 vehicles. The forms for body panels are expensive to produce. CI has already spent $750,000 on them, and must spend another $250,000 in order to finish them. Worst of all, because every car has distinctive styling, the forms are completely useless except for stamping out the Honda SUV. CI expected to be paid $1000 for every set of panels it produced. It costs them $600 in materials and $300 in labour to produce each set. Honda is still willing to honour the price, but will not order more than enough for 10,000 vehicles. The owner of CI, Mr. Rajesh Prasad, must decide whether to finish the Honda panels or not. His two sons, Rajiv and Manoj, have the following opinions. Rajiv: "If we continue, we will have spent $1 million for the Honda forms, and that is exactly what we will make in net revenue on them: $100 per set times 10,000 sets of panels. That's no return on our money at all. We'd be better off using the $250,000 in our ongoingMaruti contract. We only make 5% per annum on our investment in that business, but it is better than nothing!" Manoj: "We're better off finishing the Honda deal, even if we won't make as much money as we thought we would." Whose advice should Mr. Prasad take? Q4. Suppose that Saregama India Limited, the music company, has the copyright to the latest pop album of the band Euphoria. The market demand curve for the album is Q = 800 - 100p, where Q represents quantity demanded in thousands and p represents the price in dollars. Production requires a fixed cost of $100,000 and a constant marginal cost of $2 per unit. a. What price and sales shall maximize profits for Saregama? b. What is the maximum profit? c. Calculate the Lerner Index at the profit-maximizing scale of production. d. Suppose that the fixed cost rises to $200,000. How would this affect the profit-maximizing price?05. Suppose that indigo Airlines has amonopolv on the route between Delhi and Goa. During the winter [November - February], the monthly demand on this route is given by P: a. - bQ. During the summer {March - June], the monthly demand is given by P = it; - .59, where cram\". Assuming that [ndigo's marginal cost function is the same in both the summer and the winter, and assuming that the marginal cost function is independent of the quantity Q of passengers served, will Indigo charge a higher price in the summer or in the winter? '06. [n M G Road, Bengaluru1 the movie market is inonopolistically competitive. The demand function for daily attendance and the longrun average cost function at the INOX are, respectively. P = 9 0.4Q and LAC = ID 0.060 +0.0IDO IQ3 a. Calculate the price that [NC-X will charge for admission to movies in the long-run. What will he the number of patrons per dag.r at that price? it. 1What is the value of LAC that the firm will incur? How much profit will the firm earn