Question

8. Fats Dominio's preferences over food expenditures, (f) and expenditures on other goods (g) can be represented by the utility function: Fats 3/4 1/4 with Slim Picken's preferences can be represented by the utility function: Slim 1/4 3/4 with Slim Each has income of only $100.00 per month: the competition from the pop idols and hip hop has really urt sales. Prices are pf - Pg -1 (a) What are the optimal expenditures on food and other goods for both Fats and Slim? (b) On ONE diagram draw the budget line for both Fats and Slim. Indicate the optimal consumption bundle for Fats and for Slim. Make it big and read below for what else will be on it! (c) Since a measly hundred bucks a month can hardly keep Fats and Slim in the style to which they have become accustomed, the Government decides to give each $50.00 worth of food stamps. One dollar worth of food stamps can be redeemed for one dollar of food. What is the new budget set for Fats and Slim? Show it on your diagram (d) What is the optimal point under the Food Stamp program for Fats? For Slim? Would either prefer $50.00 in cash rather than $50.00 worth of food stamps? Indicate the optimal point on your diagram and include the indifference curves that the optimal points lie on. (e) At the optimal food stamp choices, what are both Slim and Fats' MRSgf? Is the food stamp program Pareto Optimal? Can you infer anything about the potential for a black market? WHY? Who will sell what to whom? What is the minimum price of food stamps? The maximum?

Answer 1

MRS_gf^Fats = 3g/f, MRS_gf^Slim = g/3f, M = 100, p_f = p_g = 1 a) at optimal expenditure level MRS_gf = p_g/p_f = 1 so for fats, 3g = f. B.C. rightarrow fp_f + gp_g = 100 = M rightarrow f + g = 100 so put f = 3g, thus 4g = 100, (g^* = 25, f^* = 75) for fats. for slim, g = 3f so put g = 3f, in B.C. 4f = 100, f^* = 25, g^* = 75 Ans b) Both have same B.C. with slope 1. (c) food stamps of $ 50, Now New Budget Set Now Max possible f^* = 50 + 100 = 150. thus kink at point (50, 100), when entire income is spent on g, one still can have f = 50. \r\n d) Now Eqn under Food Stamp Program, fats get more utility from f, so prefer more f than g. Slims like more g, so they