please answer the question below

Quest ion 1 Avery just graduated from Georgetown and works as a Consultant in Washington, DC. Avery has preferences over streaming service; 3:, and meals at fancy restaurants, y, represented by the following Cobb-Douglas util- ity function: U(:I:, y) :55 91%. Avery' s rm wants to promote her to a higher position that involves moving to New York City (NYC) Suppose that Avery's only source of" 1ncome is her current wage,w 11130, and that her labor supply is inelastic and equal to 1, l = 1 (we assume she doesn't value leisure at all). (i) Derive Avery's indirect utility as a function of any given prices and her wage, v(pr, pg, w). Hint: First, derive the demands for :1: and y at prices pm and 10,, and then substitute them in Avery's utility function. (ii) Suppose Avery's wage in DC is wDC 60, the price of streaming services is 132 1 and fancy meals cost pg = 8. Calculate Ann's utility from working' 1n DC, no . (ii) Now suppose Avery is offered the position in NYC. Avery's utility function is the same in both cities, the price of streaming services is the same, however fancy restaurants are far more expensive. Avery receives an initial wage offer of wNYC 100. Assume that the price of streaming services is the same in both cities, but the price of fancy restaurants is p,,- 27 in NYC. Calculate Avery's utility level if she took the job offer and moved to NYC, 11.1. Will she take the offer? (iii) Looking to receive a counter-offer, Avery argues that NYC is too expensive. Calculate the Equivalent Variation from moving to NYC at the same wage level of $60 in both cities. Interpret your result. How can Avery use this result to argue for a counter-offer? (iv) Suppose the rm's HR team in NYC knows Avery's preferences. Calculate the wage offer she will receive if the rm wants to keep her utility at the same level she gets from working in DC