COMM 295 Assignment 1 SOLUTIONS

# A write the equation for her budget line 2 pts budget

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a) Write the equation for her budget line. (2 pts) Budget Equation: 4A + 2T = 20. b) If Connie's utility function over these two goods is given by U(A,T) = 5A + 2T, draw a graph. (Put T on the horizontal axis and put A on the vertical axis.) Show the combination of A and T that maximizes her utility subject to her budget constraint. (Hint: A and T are perfect substitutes for Connie.) (4 pts)

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7 MRS = -MU T / MU A = -2/5. Since MRS is constant, the two goods A and T are perfect substitutes for Connie and her ID curves are straight lines. The slope of BL, MRT = - P T /P A = -2 /4 = - 1/2. Since the MRS is less than the MRT in absolute value, ID curves are flatter than BL. As shown in the graph, the utilizing-maximizing bundle (subject to her budget constraint) is given by T = 0 and A = 5. c) Now assume that there is a special promotion for tomatoes. If Connie buys 5 kgs of tomatoes at the regular price, she gets the next 2.5 kgs for free. Any additional tomatoes cost the usual price of \$2/kg. Draw her budget line under this new promotional scheme. (4 pts)
8 d) Will this new promotion scheme change Connie's utility-maximizing bundle? Draw a diagram to show her new utility-maximizing bundle. (5 pts) With this promotion, Connie can maximize her utility by moving from point X to point Y on the graph. So she will take advantage of the promotion and buy 5 kgs of Tomatoes (and 2.5 kgs of Avocadoes) to get 2.5 kgs of Tomatoes for free . e) Instead of linear indifference curves, Wei has indifference curves that exhibit a diminishing marginal rate of substitution. Use two diagrams to show that this promotion may or may not increase Wei’s consumption of tomatoes. (5 pts)

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