Question

Question 3: After winning the lottery, Australian Artie decides to retire, stay home, and watch sports on television all day. Artie likes both Rugby, R, and Aussie Rules Football, F and views them as imperfect substitutes. In particular, Artie's preferences can be represented by the follow- ing utility function: u = R04Fs. Since Artie is rich, the only cost of watching F is the opportunity cost of not watching R: one hour of R necessarily means one hour less of F. In other words, even though Artie is rich, there is still a price on his time. (a) What is Artie's marginal rate of substitution between R and F, MRSRF? Interpret it. (b) What is the price ratio, pa/pr? Interpret it. (c) Suppose Artie chooses some bundle, (R, F). If this bundle maximizes Artie's utility, what relationship must hold between R and F? MU& be equal to? should find actual numbers.] (d) DefineMus, What is the interpretation of this? If Artie is maximizing his utility, what must PR e) Suppose there are 24 hours in a day. What bundle (R, F) wl Artie consume? [Now you

Answer 1

Given that, The utility function U = R^OH p^0.6 MRS_RF = partial differential u/partial differential R/ partial differential u/ partial differential F = squareroot 4 (R)^-0.6 (F)^0.6/squareroot 6 (R)^0.4 (F)^-0.4 = 2/3 F/R Interpretation, MRS shows that along an IC (keeping utility level unchanged) The rate at which a consumer can give up some amount of one good in exchange for others prince ratio P_R/P_F = 1 (in terms of opportunity It represents the market determined cost trade off between two goods at utility Max bundle, MRS_RF = P_R/P_F 2/3 F/R = 1, so 2F = 3R MU_R/P_R rightarrow Marginal utility obtained from watching rug by, by spending an additional hour, at utility must get same MU from watching F (or) R, when an additional hour is spent at equation 2F = 3R F = 3/2 R 3/2 R + R = 2H 5R = 48 R = 9.6 hours (R, F) = (9.6, 14. 4)