MICROECONOMICS I REVIEW QUESTIONS SOLUTIONS 1.i. 1.ii. 1.iii. 1.iv.
1.v. 1.vi. 1.vii. 1.vi. 2.i. FALSE. The negative slope is a consequence of the more is better assumption. If a consumer consumes more of both goods, the indifference curve must shift right, implying a higher level of utility. Therefore the indifference curve has to be negatively sloped. 2.ii. FALSE. If you know the slope, you can know only the ratio of the prices of the two goods. 2.iii. FALSE. An increase in the price of good X may decrease the consumption of good X while increasing the consumption of good Y, if both are normal goods. See graph below. Consumer moves from point A to C.
3.i. Assume P=1 for composite good. 3.ii. The opportunity cost of an additional unit of the composite good is equal to how many Biskrems you have to give up in order to consume that additional unit, that is, ratio of the prices. Pb=2.5 Pc=1 Opportunity cost= 1/(2.5)= 0.4 units of Biskrem 4. Potatoes, spaghetti. 5.i. The bundle (10,5) contains 10 units of food and 5 of clothing. Suat receives a utility of 10(10)(5) 500 from this bundle. Thus, his indifference curve is represented by the equation 10FC 500 or C 50/F. Some bundles on this indifference curve are (5,10), (10,5), (25,2), and (2,25). It is plotted in the diagram below. Melis receives a utility of 0.2(102 )(52 ) 500 from the bundle (10,5). Her indifference curve is represented by the equation 0.2F 2 C 2 500, or C 50/F. This is the same indifference curve as Suat. Both indifference curves have the normal, convex shape. 5.ii. For each person, plug F 15 and C 8 into their respective utility functions. For Suat, this gives him a utility of 1200, so his indifference curve is given by the equation 10FC 1200, or C 120/F. Some bundles on this indifference curve are (12,10), (10,12), (3,40), and (40,3). The indifference curve will lie above and to the right of the curve diagrammed in part i. This bundle gives Melis a utility of 2880, so her indifference curve is given by the equation 0.2F 2 C 2 2880, or C 120/F, again to the right of the curve in part i. 6. You won t be held responsible for this question.
7. Here is the utility maximization problem: (Take q1=x, q2=y)
9. An inferior good is a good whose demand decreases as income increases. That means a negative income elasticity. A normal good is a good whose demand increases as income increases. Then the income elasticity of a normal good must be larger than 0. A luxury good is a normal good whose income elasticity is larger than 1. This means that when income increases by some X%, the demand for the luxury good must increase by Y%, Y>X. A necessity good is a normal good whose income elasticity is smaller than 1 (but obviously larger then 0 since it is a normal good). when income increases by some X%, the demand for the necessity good would increase by Y%, Y<X. A good cannot be both a normal and an inferior good for the same person at the same time, but a good can be a normal good for one person while it is an inferior good for another person, mostly depending on their income levels and preferences. 11. You won t be held responsible for this one as well. No elasticity in the exam. 12. Half a sliced banana= 1 unit of good 1, let s call it B. A bowl of cereal is 1 unit of C. U= min[b,c] B=C Plug this into the budget constraint. M=Pb*B+Pc*C= Pb*B+Pc*B= B(Pb+Pc)=M B=M/(Pb+Pc) 13. Olivia consumes one piece of pie (P) together with 1 ice cream, (I). These are complement goods. So Olivia s utility function is then U(P, I) = min{p, I}. Utility is maximized only when P = I. Her budget constraint is p P * P + p I *I = M. Substituting P=I into the budget constraint yields P = M / (p P + p I ) This is Olivia s demand function. In order for her to consume 1 more piece of pie, her income should rise by a total of p P + p I, because in order to consume 1 more piece of pie she always must consume 1 more ice cream.
18. x/y is the ratio of quantities consumed of x and y, so his utility level will be constant as long as this ratio is constant. His indifference curves are positively sloped straight lines. 20. Max s MRS= - MU x / MU y = - (y+1) / x We equalize MRS=Px/Py (y+1)/x=2 Budget constraint 10=2*x+1*y So we solve these two equations together and find that x=11/4 and y=9/2. If Max s income doubles and prices stay unchanged, his demand for both goods does not double. The proof is that if quantities of both goods doubled the MRS would not stay the same. Price ratios are constant (2/1), which would not be equal to MRS. 21.a. Pick a utility level, say U(x,y) = k = x + 2y. Then we can write y = -1/2 x + 1/2 k. This is a line with slope -1/2 and y-intercept 1/2 k. If we set k = 6, we get the solid line labeled U = 6, and if we set k = 12, we get the dashed line. 21.b. This is perfect compliments, the L-shape. Here we draw the ray from the origin, x = 2y, or y = 1/2x. The L-shape will be along this line.
21.c. In this instance, the shape is like a 7 as opposed to an L, and we simply choose the larger. Again, we draw the ray from the origin, x = 2y, or y = 1/2x. The 7-shape will be along this line. 24. Refer to the solution for question 29. 29. U=X*Y+X+2*Y+2 MRS = - MU X /MU Y = - (Y+1)/(2+X) = - 2 Y 2X = 3 If X = 10, then Y must be equal to 23.