Assume that a consumer is faced with a market basket for pizza (P) and burritos (B) with price/unit Pp=1 and P-2, respectively. The maximizing market basket (point A) must satisfy two conditions: 2a. It must be located on the budget line (meaning affordable). 2b. It must give the consumer the most preferred combination of goods and services. Show graphically the point (point A) that maximizes satisfaction/utility and satisfies conditions 2a and 2b. Show mathematically this point that maximizes satisfaction/utility.
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- Assume the budget constraint and the indifference curves are both linear. Assume the consumer is willing to tradeoff 1 of good X for 1 of good Y. If the relative price of one additional good X is giving up 1/2 of good Y, then the optimal bundle of the two goods is any combination on the budget constraint all Y 1 of X and 2 of Y all XSuppose a consumer has a budget of $200 to spend on two goods, X and Y, whose prices are $20 and $10, respectively. If the consumer is observed to buy 5 units of X and 10 units of Y, where the respective Marginal Utilities of X and Y are, 50 and 40 utils, is the consumer in equilibrium? Explain why or why not. If the consumer is not in equilibrium under conditions in d), suggest another combination that would possibly achieve equilibrium. Explain your answer.The MRS of food (vertical axis) for shelter (horizontal axis) measures the amount of food that must be received in order to absorb the loss of 1 unit of shelter without losing utility. If that value is 3, if the price of food is 5, and if the shelter price is 10, then the consumer is not maximizing his utility. Sketch a budget line, assuming the consumer has $100 to spend, and draw in a possible indifference curve that illustrates the situation described here. Then, on the same graph, show with a simple sketch what could be done to correct the problem.
- Joyce consumes x1 and x2 together in fixed proportions. She always consumes 1 unit of x2 for 2 units of x1. What is the utility function that describes her preference?You have the Cobb-Douglas utility function u(x,y) = xy over apples (x) and plums (y) and you have $120 budget to spend and can carry at most 480 ounces in weight in your backpack going back to the dorm. Each apple costs $1 and weighs 8 ounces, and each plum costs $3 and weighs 4 ounces. You can only leave the store with a bundle of fruits you can afford and carry. (a) Drawing the relevant lines, intercepts, marking the points and hence identifying the feasible set of bundles, calculate the optimal bundle. (b) Forget about (a). If you were to choose a backpack before going on this shopping trip, for the weight constraint not to be an issue for you, how many ounces of weight capacity would you need for your backpack? HINT: That is, for this weight capacity of the backpack, you’d be able to carry the best bundle you can afford, i.e, the weight constraint is not binding for your decision. ( c) Forget about (b). In (a), just before going out for shopping with your backpack to buy the…Suppose the utility function for a consumer is given by U = X + Y, where X and Y are a consumer's consumption of goods X and Y. Which of the following bundles does this consumer find indifferent between 10 units of X and 5 units of Y? You Answered a. 4 units of X, 10 units of Y b. 2 units of X, 13 units of Y c. 5 units of X, 7 units of Y d. 8 units of X, 8 units of Y
- Draw a budget constraint for an individual where if all income is dedicated to consumption of good X, the consumer can consume 40 units, and similarly, if the consumer dedicates all income to good Y 40 units can be consumed. What is the slope of the budget constraint? Draw in an indifference curve for this consumer showing an initial consumer equilibrium, with consumption of X and Y labelled. Now suppose that the price of good X falls such that 80 units of X could be purchased if the consumer dedicates all income to good X. What is the price ratio and slope of the new budget constraint? Draw in a new indifference curve tangent to the new budget constraint, together with consumption of X and Y. Identify the income and substitution effects graphically.Lisa views pizzas and burritos as goods. If she prefers a bundle of 4 burritos and 4 pizzas to a bundle of 4 burritos and 5 pizzas, which property of consumer preference is violated? What change in the assumptions could lead a rational consumer to prefer the first bundle?Q1) For the utility function in part a below, draw a set of indifference curves showing utility levels U = 12, U = 16, and U = 24. U = XY What is the relationship between the two goods X and Y? (as implied by shape of indifference curves) What is the marginal utility of X? Q2) John and Sam have the same income. The stadium sells hot dogs for $4 and popcorn bags for $3. They have different preferences; John likes popcorn much more then Sam. At their optimal bundles, John and Sam’s Marginal Rates of Substitution will be: A) the same B) Sam’s MRS will be greater. C) John’s MRS will be greater. D) we cannot tell.
- Present a budget line and a budget set for the consumer of two good X and Y, where the consumer has an income of $3,000 per month. Assume the price of X is 2 and the price of Y is 6. Suppose the price of Y decreases to 4. Show how your budget line changes and use your diagram to explain why the price decrease will make the consumer better off. Add at least two indifference curves, using them to show how the decrease in price will change the optimal choice, assuming the law of demand holds for good Y.* Kate loves cookies and chocolates. The price of cookie is $1 per piece for the first 10 pieces and $4 per piece thereafter, while the price of chocolate is $2 for the first 10 pieces and $10 thereafter. a) Kate’s has income $100. Placing the cookie on the horizontal axis and chocolate on the vertical axis, carefully sketch the budget set for Kate. Be sure to plot and label points of interests (such as kink points, intercepts and the slopes. b ) Suppose cookies(x1) and chocolates(x2) are perfect substitutes to Kate, and she is always willing to substitute two cookies for one chocolate. De- rive Kate’s utility function. c) Giventheinformationabove,findKate’sdemandforcookiesandchoco- lates. please express final numerical answers in decimal formatA consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 15 and the marginal utility of Y is 8. The unit price of X is $3 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should Multiple Choice a. decrease consumption of product X and increase consumption of product Y. b. increase consumption of product X and increase consumption of product Y. c. decrease consumption of product Y and increase consumption of product X. d. stick with the current consumption mix because it yields maximum utility.