Intermediate Microeconomics I ECON 2000 (EC20A) Tutorials Exercise sheet 4 1. Ex

Question

Intermediate Microeconomics I ECON 2000 (EC20A) Tutorials Exercise sheet 4 1. Explain the relation between the marginal rate of substitution and the relative price of goods, when the consumer maximizes his satisfaction. 2. Although many consumers indicate a preference for BMW automobiles, explain why they tend to buy Toyota. 3. Suppose that two consumers A and B buy two goods, food (F) and clothing (C). Consumer A's preferences are represented by the utility function U(EC) = 5"F while consumer B's utility function is U(FC) 0.05F C Using a graph with F on the horizontal axis and C on the vertical axis, show the set of points that give consumer A the same level of utility as the bundle (F.C) a. (10,10). Do the same for consumer B on a separate graph. b. On the same graphs, identify the bundles that give consumers A and B the same level of utility as the bundle (F.C) (15,12. c. Do the consumers A and B have the same preferences? Explain. 4. A consumer has a monthly income of 1000 dollar that he allocates among two goods: food and clothing. Suppose the price of clothing is pc-50 and the price of food is Pr 20. a. Illustrate the various combinations of food and clothing the consumer could afford with his budget. Place food on the horizontal axis. b. Assume that the consumer's preferences can be represented by the utility function U(F.C) FIC1 Calculate and illustrate graphically the consumer's optimal choice. C. Suppose now that food is taxed, causing the price to increase by 50%. Calculate and illustrate graphically the consumer's new optimal bundle. d. Suppose instead that food is rationed at a quantity less than the consumer's desired quantity. ustrate the consumer's new optimal bundle.

Explanation / Answer

1) Marginal rate is substitution is the rate at which consumer is willing to give up units of good 2 to get more units of good 1.

Price ratio is the ratio at which market is willing to sacrifice one unit of good 2 for one unit of good 1.

A consumers satisfaction is maximised when these two are equal. MRS is less/more than price ratio, he needs to consume less/more units of good 1 and more/less units of good 2 so to maximize his utility. Also equilibrium occurs when rate at which consumer is willing to sacrifice is equal to rate at which market is willing to sacrifice.

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