3. Cost of living adjustments and substitution effects: (Time: 15 minutes) Rackspace (a cloud-computing company) is relocating an engineer from San Antonio to San Francisco. Because of the difference in prices between San Antonio and San Francisco, Rackspace is offering a relocation premium to the salary of the engineer. To determine the size of the premium, the company uses the engineer's consumption bundle in San Antonio (given prices here), calculates the cost of buying this bundle in San Francisco, and then offers a premium exactly equal to the difference. Is this is the smallest premium that Backspace could offer that would not make the engineer worse off from relocating? Why or why not? How would the amount by which one could reduce their calculated premium depend upon the nature of the engineer's preferences? Support your answers with appropriate diagrams and explanations. (Hint: Lookup substitution and income effects of a price change, with application to cost of living adjustments and to substitution bias of the Consumer Price Index.)