(Figure 1.9) The slope of the line between points L and M is: Multiple Choice O O O 0.67. 1.20. 0.75. 0.80.

4 Part Question on Caesar   * * PART 1 * * Caesar has preferences that are described by the utility function u = 3x 1 + 5x 2. Caesar strictly prefers the bundle (x 1, x 2) = (0, 6.6) to the bundle A. (3, 3) B. (5, 3.6)   C. (0, 8.4) D. (11, 1.8) E. (8, 3.60)     * * PART 2 * * What is the functional form of Caesar’s preferences, or indifference curves? A. Linear (perfect substitutes)                    B. Leontief (perfect complements) C. Satiation D. Concave, but not strictly concave          E. Cobb-Douglas     * * PART 3 * * Caesar’s preferences are A. strictly convex. B. definitely not well-behaved. C. definitely well-behaved. D. strictly concave. E. neutral.     * * PART 4 * * Caesar has been consuming the bundle (x 1, x 2) = (10, 2.4). At this point, what is the marginal rate of substitution? A. – 0.25 B. –0.6 C. – 1.67 D. – 3.0 E. – 5.0.

D E B 04 What does point D on this graph represent? O An optimal choice O A choice on the budget constraint O An impossible choice given the income O A choice that would result in income left over

Graphical and Intuitive Optimization Consider a consumer who must allocate their available income between the consumption of two goods, Beer and Pizza.  Their preferences over Beer and Pizza adhere to the usual assumptions we have made about preferences. The indifference curve map below reflects their preferences and the budget constraint reflects current income and prices. In the simplest terms possible, define or explain the term "Marginal Utility of Beer" (MUB). In the simplest terms possible, define or explain the term "Marginal Rate of Substitution of beer for pizza" (MRSBP). In the simplest terms possible, intuitively explain the meaning of MUB/PB, where PB represents the price of one unit of Beer.

4 Assume that a person's utility over two goods is given by U(g1; g2) = g1 + ln g2. The price of good g1 is equal to p1 and the price of good g2 is p2. The total income of the individual is given by I. The marginal rate of substitution between g1 and g2 is given by 1/(1/g2). Then, the expressions for this person's (1) budget constraint, (2) budget line's slope (assume that, graphically, g1 is on the horizontal axis and g2 on the vertical axis), and (3) the person's demand function for g2 (that is, g2 as a function of price ratio) are respectively:

A consumer has preferences over bundles of two goods with indifference curves defined by X2 = for k>0. (a) Find a utility function representing these preferences assuming that the consumer's pref- erences are monotone. (b) Give an example of a utility function representing non-monotone preferences with the same indifference curves. (c) Show that indifference curves of the form x2 = x + k for k € R cannot arise from monotone preferences.

(b) It is thought that a consumer measures the utility, u(x, y), of possessing a quantity, z, of apples and a quantity, y, of oranges by the formula u(x, y) = rªyla, where a is a constant. Suppose that apples cost p dollars each and oranges q dollars each. If the consumer has M dollars to spend on apples and oranges, use the method of Lagrange multipliers to find the quantity of each that he will buy in terms of a, p, q and M. [You are not required to justify the use of the method of Lagrange multipliers here.] For equally priced apples and oranges when he has one dollar to spend, he is actually observed buying one apple and two oranges. What value of a does this imply?

Refer to the information provided in above Figure: The slope of the line between Points A and B is: O a. 1.5. b. -0.67. O c. -1.5. O d. 0.67. پار Units of Y 2 D 3 6 B 9 Units of X 12

The consumer choice is not restricted to the choice of consumptiongoods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has awage per hour of 10 euros. With her earned income she consumes. That isC=wH per day.She also decides how many hours to work of take leisure time each day.H=24-N, whereHis work and N is leisure. Her utility is given by （picture） Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif-ferent curve. What is the labor supply function?

PROBLEM (1) Suppose a consumer has just enough money to afford the bundle of 3 apples and 2 oranges, and similarly she also has just enough money to afford the bundle of 2 apples and 4 oranges. (a) Denoting the number of apples with x and oranges with y, plot the two given bundles on a graph, and calculate the relative price of apples; px/ py. (b) If she buys only apples with her budget, how many can she buy? If she buys only oranges, how many can she buy? Write down the budget equation for the consumer. (Notice that knowing two points on the budget line, you can write down the budget equation, even though you weren't given the prices nor the income explicitly!) (c) Suppose MUx = 20 and MUY = 30 at some point on the budget line. Is she maximizing utility by choosing this bundle? If not, should she buy fewer apples (and more oranges), or more apples (and fewer oranges), to increase her utility? (d) Forget about (c); instead, you learn that her utility function is u(x,y) = Axy³. What is…