Question

Please help me problems 5 e, f and g

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(P, P, 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

Giveen; V(,4) - D4323; P=1; R = 10 ; M=90 . i. Her budget constraint a DXIOL = M (M = Budger) - i e) Now equilibrium condu: MRSPL - Pp or, MUP-Po MUL PL ov, 4 D-43472 . PVBL-13 - or, D=54-① or, 1 . 1 = 11 15 the Euger Sotling ② in ①; we get 15L-M ork= M - volüch is the Engel Curue for Live music, Eugel funch rop=MI as the ① an Similarly from we ger? D = my L 3 for downloaded trade LED i p Eurome Elasticity for good "x": Om Fore; OL.M= M = U - aM [ 15. m/ob 24 eleistic, ok are mir inome Clearly, both goods 9 - Mechanisms like autians often reveal there are up true willinguess to pay o) Alo, & a financial advisovo can ask for are's expenditure and inoue dara, • Incentives in the form of new and can abo help

Gian V4) - DV8173; P=1) - 10;M=90 o Her Fudger constraint D+ IOL-M (M-Budger) - ) Now equitibus cond: MRSPL - P or MUP PP MUL PL ov, D-7392 id DVBL- V ori 15 ov, zbió ov,D=54- Sotling in woe geri 15L=M ork- M - vollich is I the Engel Curne for Live Music, Similarly from 1 an ; we ger: D = M as the Eugel funch I for downloaded trouble + Trome Elasticity for good "x"; one tuen M ForLi om MBT For D mir imone eleistic, Clearly, both goods are 9) - Mechanipuis like autious otten reveal that one's true voitti uguess to pouy, a) Also, yo financial adviporo can ask for are's expenditure and imame dara, • Incentives in the form of newamp can abo help-