Question

Please help!

5. Katie enjoys downloading music tracks and attending live music. She pays PD = $1 per downloaded song and PL = $10 per unit of live music (entrance fees to clubs). She has $90 per month to spend on music. Her utility function for music is U=D1/L2/3, where D represents the quantity of downloaded songs and L is live shows. a. Use either the Last Dollar Rule (use-the-graphs pg 35) to find Katie's optimal mix of music b. What is Katie's level of utility at the optimal mix? c. One of the weaknesses of using actual dollar values for prices and income is that you cannot find Engle and Demand functions. Go back to part a, but use the parameters M for income, PD for price of downloaded songs and PL for price of live music and solve for the demand of downloaded songs, Qp = D(PD, PL, M). d. Use the functions you found in part c to take derivatives to show mathematically if downloaded songs are: i. Normal or inferior? ii. Ordinary or Giffen goods? iii. Are downloaded songs and live shows substitutes, compliments or unrelated? Note, the derivative of DD(M, PP, PL) with respect to Pp is tricky, so don't worry if you have difficulty, give it your best try but don't stress out. e. Graph the Engle curve and the Demand curve for Downloaded songs on separate axis using several prices and income levels. f. Find the income elasticity of demand using the Dd function you found in part c and a formula similar to the one two-thirds down on page 58 in the text. g. The hardest relationship/function to find in this problem is the utility function (income and prices are easily observable). How would you set up an experiment to gather data on someone's utility function?

Answer 1

JAst dollor uli 2. MO MOn 1. 2x 0'3 3810X1/3 D43 5L 90 0 +1oL 90= SL+loL 90=152 L= 6 D= SL=6x5=30 7x. (3orex6) = 10.25 U= log0/3 MUD MUL 2x0/3 3X3XPL भऊ 3.0 3xcH3Xf 2PD M= 2.D:PD xP t Do Po Mz 20.Po + DPo O M Demand downlond Sorgs/ M2RL+P.L 2. M=l5 P.I Demand L=shlive Songs 2020.01.20 23:50

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