Suppose a consumer tells you that she strictly prefers bundle x to bundle y. If the consumer's preferences satisfy monotonicity and transitivity, which of the following can we conclude? (Check all that apply)
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- 3.7 a. A consumer is willing to trade 3 units of x for 1 unit of y when she has 6 units of x and 5 units of y. She is also willing to trade in 6 units of x for 2 units of y when she has 12 units of x and 3 units of y. She is indifferent between bundle (6, 5) and bundle (12, 3). What is the utility function for goods x and y? Hint: What is the shape of the indifference curve? b. A consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle (8, 1). She is also willing to trade in 1 unit of x for 2 units of y when she is consuming bundle (4, 4). She is indifferent between these two bundles. Assuming that the utility function is Cobb-Douglas of the form U(x, y) = xy, where a and 3 are positive constants, what is the utility function for this consumer? c. Was there a redundancy of information in part (b)? If yes, how much is the minimum amount of information required in that question to derive the utility function?Carol has very weird preferences. She only cares about quantity. When evaluating a bundle, Carol only looks at the highest amount of a good she can consume in each bundle, regardless of whether it is of eggs or dumplings. She is indifferent between two bundles only when the largest consumption of a good within each bundle is the same across bundles. So, for instance, if a bundle offers 5 eggs and 1 dumpling she finds that bundle indifferent to a bundle offering 4 eggs and 5 dumplings. These preferences are transitive. But are they monotone? And convex?1. Doug consumes two goods, electricity, e, and a composite commodity z. Doug has the following utility function: U = z²-e Last week, he clicked on a Facebook ad and got free solar panels put on his roof! Now Doug has solar panels on his roof that generate 50 units of electricity per day. For the going price of electricity, if Doug demands more than 50 units of electricity, he can buy more at that price. If he demands less than 50 units, he can sell the extra electricity (50 - his consumption) back to the grid, and earn the going price as extra income. a. What are his Marshallian demand functions for e and z? b. Currently, Doug's income is $100 per day, the price of z is $1 and the price of electricity is $0.50. How much electricity is he consuming and what is his utility? (note, the utility numbers may get a bit large). C Calculate quantity demanded for electricity and his utility if the price of electricity rises to $1. And then calculate the quantity demanded and utility when the…
- Suppose that Joe consumes cupcakes and pizzas. The price of cupcakes is $5 per unit and the price of pizzas is $10 per unit. The table shows Joe's utility from the consumption of each good; each row represents a possible consumption bundle. Currently, Joe is consuming 18 cupcakes and 9 pizzas. A Quantity of cupcakes 10 12 14 16 18 20 22 24 26 Utility of cupcakes (utils) 50.00 68.30 81.00 89.00 93.70 96.40 97.74 98.20 98.56 Q of pizzas 5 13 12 11 10 8 7 6 9 Utility of pizzas (utils) 263.00 258.00 250.00 240.00 227.00 212.00 195.00 175.00 150.00 Show Transcribed Text n a. Calculate the marginal utility per dollar of going from eight to nine pizzas. b. To increase total utility without increasing spending, should Joe change the amount of consumption of either good? OYes, Joe should choose more cupcakes and fewer pizzas. O Yes, Joe should choose more cupcakes and more pizzas. O No, Joe is already consuming at the optimal consumption bundle. O Yes, Joe should choose fewer cupcakes and more…Suppose that Lynn enjoys sugar in her coffee. She has very particular preferences, and she must have exactly three spoonfuls of sugar for each cup of coffee. Let C be the number of cups of coffee, and S be the number of spoonfuls of sugar. Also, let PC be the price of a cup of coffee. Suppose Lynn has $12 to spend on Coffee and Sugar. Also, the price of Sugar is $.20 per spoonful. Graph Lynn’s Price consumption curve for prices, PC = $.60, PC = $.90, and PC = $1.80. Please put the number of cups of coffee (C) on the horizontal axis, and the number of spoonfuls of Sugar (S) on the vertical axis. Be sure to graph each budget constraint associated with each price of Coffee, identify Lynn’s optimal bundle on each budget constraint, and make sure your graph is labeled carefully and accurately.If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.
- Suppose you have an income of $24 and the only two goods you consume are apples (x1) and peaches (x2). The price of apples is $4 and the price of peaches is $3. Suppose that your optimal consumption is 4 peaches and 3 apples. a. Illustrate this in a graph using indifference curves and budget lines. b. Now suppose that the price of apples falls to $2 and I take enough money away from you to make you as happy as you were originally. Will you buy more or fewer peaches? Provide a graphical representation.Let's suppose that an individual prefers bundle of goods A over another bundle of goods B. Let's suppose that the individual prefers the bundle of goods C to the bundle of goods B. Then we can say the individual prefers C to A because more is better than less the individual prefers A to C because more is better than less two answers are correct no answer is correct O the individual prefers A to C; because of transitivity the individual prefers C to A because of transitivityLet the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 6 7 TUX 8 14 18 20 20 18 16 TUY 6 10 13 15 16 16 14 MUX MUY MUX/PX MUY/PY Calculate the MUX and MUY and fill the table in the 4th and 5th rows. If the two products (X&Y) are free goods how many of X and Y should the consumer take to maximize utility? What is the maximum utility of X and Y if they are free? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit. Calculate MUX/PX and MUY/PY and fill the 6th and 7th row. Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? What is the total utility of X and Y? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility?
- Question #7: There are two goods in the world: eggplants and canned peas. Canned peas are an inferior good while eggplants are a normal good. Annie's income is $20 and peas cost $1 per can while eggplants cost $4 each. Draw a graph that shows the combinations of the two goods Annie can consume (put peas on the horizontal axis and label the axes and the intercepts). Given this constraint, Annie chooses to consume 8 cans of peas. Label her preferred bundle on the graph and be clear to show that this is optimal bundle. The price of eggplants falls to $2. Explain the effect on Annie's consumption of eggplants and peas. Draw a new graph with both budget constraints, the old and new indifference curves indicating her preferred bundles and explain any income and substitution effects. 5Joe is currently in consumer equilibrium by consuming cheese and crackers, such that the last cracker consumed yielded 8 utils and the last piece of cheese consumed yielded 12 utils. Assume the price of crackers is two cents per cracker and the price of cheese is three cents per piece. If the price of crackers increases to four cents, Joe should his consumption of crackers and his marginal utility from crackers will and also his consumption of cheese and his marginal utility from cheese will (Assume he is in the downward sloping portion of the MU curve.) Ο Ο Ο decrease; increase; increase; decrease increase; increase; increase; increase increase; decrease; increase; decrease increase; increase; decrease; decreaseYou are choosing between two goods, X and Y, and your marginal utility from each is as shown in the following table. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase to maximize utility? What total utility will you realize? Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? Using the two prices and quantities for X, derive a demand schedule (a table showing prices and quantities demanded) for X.