Question

If p is the price in dollars of computer mice at time, t, then we can think of price as a function of time. Similarly, 1. then number of computer mice demanded by consumers at any time, and the number of computer mice supplied by producers at any time, may also be considered as functions of time as well as functions of price. Both the quantity demanded and the quantity supplied depend not only on the price, but also on the rate of change for price in terms of time. Suppose the supply and demand functions for computer mice, in hundreds of units, are given by: dp 30 p5 Supply Equation: q dt dp Demand Equation: q 51 2p+ 4 = dt dp Where dt denotes the rate of change of the price with respect to time. Use the above equations to answer the following questions. Assume that the market equilibrium price is $12 initially: Find the market equilibrium price as a function of time. Start by setting the quantity equations equal and a. solve for Then multiply both sides by dt and integrating each side according the domain variable indicated. Finally, solve for p to get your price function dt b. Use limits to determine if there is a price stability in the marketplace for the computer mice. Basically find the limit of p as time approaches infinity. If there is a limit, state the price. Using the dt and the p functions from part (a), find the equilibrium quantity function by substituting c. those afore mentioned into one of the original quantity functions. d. Do part (b) over using the equilibrium quantity function and if there is limit, state the quantity.

Answer 1

Supply fun lan Pemand functien, =30 + P+ 5 dp ar51-2P+4 ar df 30+p+5 dpS1-2p+ 24-3P--3(P-7) -) dp 3dt a) At equilibrium skage dp -3t ic P 7t e P-70 An (P-7) 3 P-7e S4 S- dP ア-7 3dt rl market equilliium prica at intenly is 12 P= 12 atそ=0. From , Givaり t2 7+e e =5 c- An5 )=CTIN -3 Pe 7+ es e Pe 7+ 5e lim (7+5e) b) im P- tod 7+ SO)- 7. e audd dp dt 21-3P. c we thave a30t PtSdP 31 but pzワ+Se 314P 3t wwww.kga 3b+P+S(21-3P) 37-70 e AD O -3t Lim (37-70 e) TeNT 37 37-0 d n ta 605 004 7to- -