2. Over the past six months the inflation rate, which measures the changes in the price level, has been of particular interest given the pandemic related supply bottlenecks and Fed monetary policy. One complication with measuring inflation is that different prices change by different amounts and sometimes in different directions (for example, the price of college tuition has been steadily rising for decades, whereas the price to smartphones has been decreasing). We can use the expenditure function to aggregate the change in the price level, by asking how much more it costs to achieve the same utility level under the new prices. That is if the price increases from (:01, p2) to (pim) we can define the inflation rate as: i: EQ'LPE: U) _ 50311152: U) 1 15071le U) Suppose Ella has Cobb-Douglas utility, U = 3q13q23, and an income level of Y = 600. Suppose p1 = 100 and p1 = 100 so the price of good 1 doesn't change, but the price of good 2 increases from p: = 25 to p5 = 64. 3. Calculate Ella's optimal consumption bundle and utility level at the initial prices p1 = 100 and p2 = 25. b. Solve for the income level Ella would need to achieve the same utility level under the new prices pi = 100 and p; = 64. c. Given your answer to part (b) what is the inflation rate for Ella given the price change? d. In practice, economists can't observe utility functions but only the consumption levels chosen. For this reason, it is necessary to try to apprOximate the inflation rate using consumption levels. One approach is the Laspeyeres price index which calculates how much more money would be needed to afford the initial consumption bundle, (1.1031, :02) and (130),, 1);), at the new prices: = 10311091. 102) + pq; (:21. p2) p14; (:91, p2) pzq (171,192) Ll . . p1q1(p1.p2)+ pzqzmmz) Calculate the Laspeyere's price index for Ella when the price of good 2 increases from 25 to 64. 8. Does the Laspeyres price index over or under estimate the inflation rate? Illustrate on a graph, using roughly drawn indifference curves and budget constraints, and briefly provide an economic intuition (no more than 3 sentences) for your answer in terms of the substitution effect. f. An alternative measure is the Paasche index, which calculates how much more money would be need to afford the new consumption bundle, (303143;) and (091, p5) at the new prices than the old prices: : piqpim) + pqpi. p5) mQIOJLp) mar-2091. p) PI r f t f f 191% (391- p2) + 92% (191,392) Without doing any calculations. would you expect the Paasche index to over or under estimate the inflation rate? Briefly support your answer with no more than 3 sentences