Section 3.7: (page 218) Worksheet (Posted on Canvas under Chapter 3 Modules)

textbrokercom C O A Not Secure Suggested Sites BusCalc.pdf ' Gmail X > '9 Final Exam YouTu be Disney+ X canvas Canvas LMS opentextbookstore.com/buscaIc/BusCalcpdf 6 find cards saved on. Untitled document-Google X 6 BusCalc.pdf X i Course Hero X 218 / 272 From I = 0 to t = l (the rst year), the income is constant $7000 per year, From t = l to l = 8, the income is increasing by $800 each year; the income ow function F(t) will be 170') = 7000 + 8000' -1)= 6200 + 800t . To nd the present Value, we'll have to divide the integral into the two pieces, one for each of the functions: . 3 PV :170002'\"'7'dt+j(6200+ soo:)a\"'dz ; 70166. a r The present value is greater than the cost of the machine, so the company should buy the machine. 3.7 Exercises 1. The demand and supply functions for a certain product are given by p = 150 .511 and p : .002q2 +1.5, wherep is in dollars and q is the number ofitems. (a) Which is the demand function? (b) Find the equilibrium price and quantity (c) Find the total gains from trade at the equilibrium price. 2. Still thinking about the product from Exercise 1, with its demand and supply functions, suppose the price is set articially at $70 (which is above the equilibrium price), (a) Find the quantity supplied and the quantity demanded at this price. (b) Compute the consumer surplus at this price, using the quantity demanded (0) Compute the producer surplus at this price, using the quantity demanded (why?) (d) Find the total gains from trade at this price. (e) What do you observe? 3. When the price of a certain product is $40, 25 items can be sold. When the price of the same product costs $20, 185 items can be sold. 0n the other hand, when the price of this product is $40, 200 items will be produced. But when the price of this product is 320, only 100 items will be produced. Use this information to nd supply and demand functions (assume for simplicity that the mctions are linear), and compute the consumer and producer surplus at the equilibrium price. 4. Find the present and future values of a continuous income stream of $5000 per year for 12 years if money can earn 1.3% annual interest compounded continuously. 51 Find the present value of a continuous income stream of $40,000 per year for 35 years if money can earn (a) 0.8% annual interest, compounded continuously, (b) 2.5% annual interest, compounded continuously, (c) 4.5% annual interest, compounded continuously. amdhno