Posted: February 10th, 2015

Inter Micro

Paper, Order, or Assignment Requirements

Inter Micro (ECON-2101) Assignment 1 • Solutions are due at the beginning of class on February 11. • Show your working, while solving the problems. • Remember to staple your answer sheets, and write your name and ID # on the first page. • All diagrams drawn must be large, clear, and properly labelled. No need to type your answers, or use graph paper for the diagrams. 1) Consider the following choice problem for a consumer who spends her entire budget on purchasing two goods, X and Y, and derives utility as given by Table 1. (i) Suppose initially prices of the two goods are = $3 x p per unit of X, and = $3 y p per unit of Y. The consumer’s budget is $30. Find the amount of X and Y in the utility-maximizing bundle for the consumer. (ii) Now suppose price of good X changes to = $6 x p . Price of good Y remains unchanged at = $3 y p , and the consumer’s budget also remains unchanged at $30. Find the amount of X and Y in the utility-maximizing bundle for the consumer. (iii) Using your answers to (i) and (ii) above, compute the price elasticity of demand for good X. Table 1: Good X Good Y Quantity consumed (x) Marginal Utility of the x th unit consumed (MUx) Quantity consumed (y) Marginal Utility of the y th unit consumed (MUy) 1 50 1 75 2 38 2 42 3 33 3 36 4 29 4 28 5 25 5 25 6 21 6 19 7 18 7 18 8 15 8 17 9 12 9 16 10 9 10 15 11 6 11 14 12 3 12 13 13 2 13 12 14 1 14 11 (4 + 4 + 2 = 10 points) Page 2 of 2 2) Consider the following utility-maximization problem of a consumer who spends her entire income on purchasing two goods X and Y. When prices and income are ( , , ) (20,10,100) x y p p M = the consumer buys bundle A where ( , ) (2,6) x y = . Then, when prices and income increase to ( , , ) (24,18,144) x y p p M = , the consumer buys bundle B where ( , ) (2.5,4.67) x y = . Does this price and income increase make the consumer better off or worse off? Explain your answer. [Note: In the above, 14/3 is approximated as 4.67. Moreover, no utility function is specified in the problem, so do not assume that it is of the Cobb-Douglas type.] (5 points) 3) A employee, who is also a consumer, has the following Cobb-Douglas utility function: 1 1 2 2 u x y x y xy ( , ) = = . The corresponding marginal utilities are 1 1 1 2 2 2 X y y MU x x   = =     and 1 1 1 2 2 2 Y y x MU x y −   = =     . Assume that the employee spends her entire salary (or income) on the two goods, and does not save. (i) Initially, the employee works and lives in Winnipeg where she gets a salary of $120 and prices of the two goods are 2 x p = and 3 y p = . What is the utility maximizing bundle for this employee in Winnipeg (call this bundle A)? What is her utility level in Winnipeg? (ii) Now suppose the employee gets transferred to Toronto where prices are 4 x p = and 3 y p = . Assuming that her salary remains $120, what is her utility maximizing bundle in Toronto (call this bundle B)? What is her utility level in Toronto? (iii) Compute the substitution effect and the income effect of the increase in x p on the consumption of good x . (iv) By what amount must this employee’s salary be increased in Toronto (from the $120 she was getting in Winnipeg) such that she is as well off in Toronto as she was in Winnipeg (i.e. compute the compensating variation of the increase in x p )? (v) How much would it cost the employee to buy bundle A in Toronto? (3 + 3 + 5 + 2 + 2 = 15 points)