Question

Assume that your utility now depends the amount of health care (h) other goods (c) and futuristic health care (f). Futuristic health care did not exist in year 1 or year 2; it was as though the price was so high that you demanded none of it. In year 3, futuristic health care is invented, and the price is $10 per unit. Meanwhile, the prices of both h and c double to $3. h. Calculate a Laspeyres price index for the changes from year 2 to year 3. Remember to use the bundle of goods (h,c) that you demanded in year 2. i. According to your result from the previous question, are you better off in year 2 or year 3 (assuming constant income)? j. In year 3, you purchase 5 units of f and 10 units of h. Explain how you might actually have more utility in year 3 than year 2 despite the Laspeyres price index result. k. How did your total health care expenditures (on both h and f) change from year 2 to year 3. l. Explain why you cannot use this result to conclude that health care is getting more expensive or less expensive.

Answer 1

Utility is a function of health care(h) other goods (c) futuristic health care (f) implies U(n, c, f) For year 2: demand rightarrow (h, c, 0) = x_2 price rightarrow (3/2, 3/2, pf) = (1.5, 1.5, pf) = p_2 Since in year 3 prices of both h & c double to $ 3, p_f = price of futuristic health care(supposedly high) For year 3: demand rightarrow (h, c, f) = x_3 since demand same as year 2 + same f prince rightarrow (3, 3, 10) = p_3 (h) Lapsers price Index = L_2, 3 = Sigma x_2 p_3/Sigma x_2 p_2 times 100 -(1) Now: Sigma x_2 p_3 = Total cost of purchasing same dd bundle of year 2 at new (current) price of y_r 3 Sigma x_2 p_3 = (h times 3) + (c times 3) + (0 times 10) = 3h + 3c = 3(h + c) And, Sigma x_2 p_2 = Total cost of purchasing old bundle of year 2, at old (base - period) price of year 2
Hope you find the answer helpful. Also, a more precise answer is possible if the consumption bundle in Year 2 is given. Since, I have started answering from part (h), I request you to once go through the question to verify the consumption bundles in all years and the utility function, if given any.

Feel free to share any doubts regarding the same. Thank you!