The CPI index is calculated for consumers with the Cobb-Douglas utility function u(x,y)= xy2 over goods food (x) and clothing (y), where the reference basket is A = (10,20) , that is 10 units of food and 20 units of clothing. The initial prices are px = py = 1 and the final prices are px = 2, py = 16. (a) Calculate the CPI (consumer price index) which is the ratio of the cost of the basket A under the final prices divided by its cost under the initial prices. (b) Naturally, given the prices increase disproportionately, we can expect the consumer not to stick with the basket A but choose another basket B where she achieves the same utility level as in A, but which costs much cheaper, under the final prices. Calculate the basket B which is the cheapest bundle under the final prices to achieve the utility level of A. Calculate the effective CPI, which is the cost of basket B under the final prices divided by the cost of A under the initial prices. This reflects the real increase in overall prices for the consumer. please answe the follwoing practice problem on a paper and uplaod if possible.
The CPI index is calculated for consumers with the Cobb-Douglas utility function u(x,y)= xy2 over goods food (x) and clothing (y), where the reference basket is A = (10,20) , that is 10 units of food and 20 units of clothing. The initial prices are px = py = 1 and the final prices are px = 2, py = 16.
(a) Calculate the CPI (
(b) Naturally, given the prices increase disproportionately, we can expect the consumer not to stick with the basket A but choose another basket B where she achieves the same utility level as in A, but which costs much cheaper, under the final prices. Calculate the basket B which is the cheapest bundle under the final prices to achieve the utility level of A. Calculate the effective CPI, which is the cost of basket B under the final prices divided by the cost of A under the initial prices. This reflects the real increase in overall prices for the consumer.
please answe the follwoing practice problem on a paper and uplaod if possible.
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