Exercise 1 ([Indifference Curves). Consider the utility function U(C1, C2) = ln(C1)+In(C2). 1. Using a program of your choice (say excel, or matlab) plot indifference curves in the space (C1, C2) for U = -0.5, -1, and -1.5. Consider values of Cị in the interval (0, 1]. Set the range of the vertical axis to [0, 2]. 2. Find an analytical expression for the slope of the indifference curve and show that it is equal to the (negative) of the marginal rate of substitution. 3. Show analytically that the indifference curves are convex. 4. For the 3 indifference curves plotted above, find the slope of the indifference curve at the point C = 1 and the corresponding value of C2. Explain why the indifference curves at C1 1 become flatter as the level of welfare declines.

If the prices for goods A & B are $5 & $12, respectively, and a customer has $200, which basket of goods (A, B) gives her the highest satisfaction that she can afford? (10, 10) We need her indifference curves (preferences) to know. (16,10) (10, 15) (15, 10)

The value in Y axis has changed from 14.94 to 10.98 and the value in X axis has changed from 9.12 to 2.29, what is the slope of the indifference curve at this point?

10. Consider the utility function U(x, y) = xy + x. Which of the following bundles is noton the same indifference curves as the others. Note: The first entry is the amount of x, thesecond is the amount of y.(a) (5,1)(b) (2,4)(c) (4,2)(d) (2.5,3)

Number of Sodas per day Total Utility Marginal Utilit 1 20 35 3 47 12 4 10 Refer to the table, The marginal utility of the second soda per day is L. (Answer should be in the form of numerical characters, e.g. 20) Enter your answer here

Henry's utility function is u(x,y)=max{x+3y,3x+y}. (a) Suppose Henry's current consumption bundle is (2,1.5), what is his current utility level? If he consumes the bundle (1.5,2), will his utility change from the current utility level?

1) (15 points) A student has a lunch utility function U(S,P) = 8S + 3P, where S is the number of salads per month and P is the number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) (5 pts.) Using the x-axis for S and the y-axis for P represent the indifference curves of the student corresponding to the levels of satisfaction U = 48, U = 72 U = 120. How does this student perceive pizzas and salads? b) (5 pts.) Find and draw the budget line of the student. Specify both the intercepts and the slope. In the same graphic, you should include the indifference curves from part (a). c) (5 pts.) Compute and represent graphically the equilibrium of the student (how many salads and pizzas he is likely to have per month). Your graph should include the budget line, the indifference curve, and the optimal consumption point.

80 60 40 20 0 a N b A 10 a Multiple Choice 20 B 30 C 40 b C NE 50 60 Refer to the diagram. The slope of curve ZZ at point A is approximately

Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.

The prices she's considering are shown in the table below. Calculate the utility for each of the prices in the table. What is the average of the calculated utilities?