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Economics 101 Summer 2011 Answers to Homework #4 Due Thursday June 11, 2011 Homework is due at the beginning of the lecture. All homework should be neatly and professionally done. Please make sure that your name is clearly legible and that you show all of your work on your homework. Please staple your homework before coming to class. 1. For each of the parts of this question use the information provided to find the consumer’s budget line. a. Mary optimizes her satisfaction when she consumes 10 books (B) and 5 apples (A) each month. Mary’s monthly income is $50 and she currently spends $10 on apples. Write Mary’s budget line in slope intercept form with books measured on the vertical axis. b. Joe can consume either 4 pizzas (P) and 10 sodas (S) or 6 pizzas and 1 soda: both of these consumption bundles lie on Joe’s budget line. Write Joe’s budget line in slope intercept form with pizzas measured on the vertical axis. c. Suzy has $100 in income and she optimizes her satisfaction when she consumes 13 books (B) and 4 (CDs). Suzy only purchases books and CDs. The price of CDs is three times the price of books. Write Suzy’s budget line in slope intercept form with books measured on the vertical axis. Answer: a. Start with the basic equation that says Income = (Price of good x)(quantity of good x) + (Price of good y)(Quantity of good y). And, plug in what you know: 50 = Pa(5 apples) + (Pb)(10 books). But, you also know that Mary is spending $10 on apples right now, so substitute 10 for Pa(Qa). Thus, 50 = 10 + Pb(10books). Solving this equation you find that the price of books is $4. You can also deduce that the price of apples is $2. Thus, the budget line is 50 = 2A + 4B or B = 12.50 - .5A. b. From the given information you know that the slope of the line that contains these two points is -2/9. Thus, the slope intercept form of the equation for this budget line can be written as P = b – (2/9)S. Then, use one of the given points in this equation to find the value of b. Thus, 4 = b – (2/9)(10) or b = (56/9). The equation for the budget line is P = 56/9 – (2/9)S. c. From the given information you know that 3Pb = Pcd. You also know that 100 = PbB + PcdCD or 100 = Pb(13) + 3Pb(4). Collecting terms on the right hand side of the equation you have 100 = 25Pb or the price of a book is $4. From this you can find the price of a CD is $12. The budget line is therefore 100 = 4B + 12CD or B = 25 – 3CD. 2. Suppose that you know the utility function for an individual is given by the equation U = XY where U is the total amount of utility the individual gets when they consume good X (X) and good Y (Y). Thus, if U = 10 then the individual can get 10 units of utility from consuming 1 unit of X and 10 units of Y (U = XY = (1)(10)) or from consuming 5 units of X and 2 units of Y or any other combination of X and Y whose product is equal to 10. Given this utility function, the MU from good X is equal to Y (that is, MUx = Y) and the MU from good Y is equal to X (that is, MUy = X). You are also told that this individual’s income is $100 and that the price of good X is $2 and the price of good Y is $4. From this information answer the following set of questions.

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