Please provide detailed instructions on how each multiple choice answer was solved. Please see attachment.

THEORY OF CONSUMER BEHAVIOR What we'll do: Understand the concept of utility and the conditions for a consumer to maximize utility subject to a budget constraint. Essential Concepts 1. The basic consumer optimization problem facing each individual can be stated as follows: Individual consumption decisions are made with the goal of maximizing total satisfaction from consuming various goods and services, subject to the constraint that spending on goods exactly equals the individual's money income. Consumer Theory: o Assumption: Buyers are completely informed (know the range of products available, the prices of all products, the capacity of products to satisfy, and their income). o Consumers must be able to rank all consumption bundles according to the level of satisfaction they would receive from consuming the various bundles. Consumer preference ranking must satisfy be both,: 1. Complete: For every possible pair of consumption bundles, A and B, the consumer can say one of the following relations holds: A is preferred to B, B is preferred to A, or the consumer is indifferent between A and B. 2. Transitive: If bundle A is preferred to bundle B, and bundle B is preferred to bundle C, then bundle A must be preferred to bundle C. Convenient (but not necessary) to add a third assumption 3. Nonsatiation: More of a good is always preferred to less of a good. 6. Utility: The benefits consumers obtain from the goods and services they consume. o A utility function shows an individual's perception of the level of utility that would be attained from consuming each conceivable bundle of goods. U = f(X, Y) o Indifference curves: An indifference curve is a set of points, representing different bundles of goods and services, each of which yields the same level of total utility or satisfaction. Indifference curves are negatively sloped and convex. If the consumption of one good is increased, consumption of the other must be reduced to maintain a constant level of utility. The marginal rate of substitution (MRS)the absolute value of the slope of the indifference curvediminishes as the consumer moves downward along an indifference curve, increasing X and decreasing Y. o Shows the rate at which one good can be substituted for another while keeping utility constant. Is the ratio of the marginal utility of X divided by the marginal utility of Y: DY MU MRS = DX MU x y where -DY /DX is the negative of the slope of the indifference curve 9. An indifference map consists of several indifference curves. The higher (or further to the right) an indifference curve is on the map, the greater the level of utility associated with the curve. 10. Marginal utility is the addition to total utility that is attributable to the addition of one unit of a good to the current rate of consumption, holding constant the amounts of all other goods consumed (MU =DU DX). 12. The consumer's budget line shows all possible commodity bundles that can be purchased at given prices with a fixed amount of money income. The relation between money income (M ) and the amount of goods X and Y purchased can be expressed as M=PxX+PyY Alternatively, the equation for the budget line can be rewritten in the form of a straight line Y =M - Px X Py Py The first term, M/Py, gives the amount of Y the consumer can buy if no X is purchased. The term Px /Py is the absolute value of the slope of the budget line. An increase in income causes a parallel outward shift in the budget line. o An increase in the price of X causes the budget line to pivot inward around the original vertical intercept. A decrease in income causes a parallel backward shift in the budget line. o A decrease in the price of X causes the budget line to pivot outward around the original vertical intercept. A consumer maximizes utility subject to a limited money income at the combination of goods for which the indifference curve is just tangent to the budget line. At this combination, the marginal 14. rate of substitution (the absolute value of the slope of the indifference curve) is equal to the price ratio (the absolute value of the slope of the budget line) DY MU x Px = MRS = - D = X MU y Py Thus a consumer allocates money income so that the marginal utility per dollar spent on each good is the same for all commodities purchase d MU x = MU y Px Py and all income is spent. 15. The demand curve of an individual for a specific commodity relates utility-maximizing quantities purchased to market prices, holding constant money income and the prices of all other goods. The slope of the demand curve illustrates the law of demand: quantity demanded varies inversely with price. 16. Market demand is a list of prices and the quantities consumers are willing and able to purchase at each price in the list, other things being held constant. Market demand is derived by horizontally summing the demand curves for all the individuals in the market. 17. Because demand prices along market demand measure the economic value of each unit of the good, a market demand can be interpreted as the marginal benefit curve for a good. Problems Problem 2, p. 194 Problem 5 p. 195 Sample test questions 5-10 According to the following figure, what could have caused a consumer's budget line to shift from ML to MN? a. b. c. d. e. an increase in the price of X a decrease in the price of X an increase in the price of Y a decrease in the price of Y cannot determine without more information Because the list of prices and the quantities consumers are willing and able to purchase at each price in the list, other things being held constant. 5-11 According to the following figure, at point A, a. b. c. d. e. the marginal rate of substitution of X for Y is greater than it is at point B. the ratio of the price of X to the price of Y is greater than it is at point B. the consumer's utility is less than it is at point B. both a and c all of the above 5-12 Marginal utility is a. the utility obtained from the consumption of all but the last unit of a good. b. the relative value of two goods when a utilitymaximizing decision has been made. c. the change in utility that results from increasing the amount of a good consumed by one unit. d. the change in the amount of a good consumed that increases total utility by one unit. e. none of the above Because. An increase in the price of X causes the budget line to pivot inward around the original vertical intercept. The consumer's income is $800. 5-19 According to the above figure, what are the prices of goods X and Y? a. PX = $10, PY = $8 b. PX = $8, PY = $10 c. PX = $100, PY = $80 d. PX = $20, PY = $60 e. PX = $60, PY = $20 By the figure Px=$8, Py=$10 5-57 Assume that an individual consumes two goods X and Y. The total utility (assumed measurable) of each good is independent of the rate of consumption of other goods. The prices of X and Y are, respectively, $5 and $10. Units of the Good Total Utility of X Total Utility of Y 50 95 135 170 200 225 245 260 400 750 950 1100 1220 1320 1400 1450 Given the above, if the consumer buys the third unit of Y, a. b. c. d. the marginal utility of the third unit is 950 units of satisfaction. the marginal utility per dollar spent on Y is 200. the marginal utility per dollar spent on Y is 20. both a and b. The Marginal utility of the commodity is the total utility of the commodity minus Total utility of one previous unit of commodity. Thus, marginal utility for third unit of Y = 950-750 = 200. Thus, the marginal utility of the third unit is 950 units of satisfaction and the marginal utility per dollar spent on Y is 200. Hence, answer to the question is D 5-1F a. b. Along an indifference curve _____utility_______ is constant. The rate at which a consumer is willing to substitute one good for another, holding utility constant, is given by the _______slope_____ of an indifference curve. This rate is called the _________________ marginal rate of substitution (MRS)________________. c. If at a given combination of X and Y, a consumer's marginal rate of substitution is 4, this means that the consumer is willing to give up ____4__ units of Y for another X or __1/4____ units of X for another Y. d. If a consumer is choosing the levels of goods X and Y in order to maximize utility with a given budget the _____MRS____ equals the ______price ______ ratio of the goods. e. The rate at which a consumer can substitute one good for another in the market is given by the ____slope__ of the budget line and is equal to the ____price______ratio of the two goods