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Assume that the data in the accompanying table give an indifference curve for Mr. Chen. Graph this curve, putting A on the vertical axis and B on the horizontal axis. Assuming that the
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- Q5. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has an income of $120; novels cost $5 each, while DVDs are priced at $15 each. [Hint: MUx=2xy2, MUy=2x2y] a) Sketch Jason's budget constraint, indifference curves and the interior solution in a graph. b) Calculate Jason's optimal consumption bundle, and his maximized utility level. Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged. c) Calculate his new optimal bundle, show it in the same graph from a), and interpret the Marginal Rate of Substitution (MRS) at this new optional bundle (point).Emily is a utility maximizer. Her income is $100, which she can spend on cafeteria meals and on notepads. Each meal costs $5 and each notepad costs $2. At these prices Emily chooses to buy 16 cafeteria meals and 10 notepads. a) Draw a diagram that shows Emily’s choice using an indifference curve and her budget line, placing notepads on the vertical axis and cafeteria meals on the horizontal axis. Label the indifference curve, I1, and the budget line BL1. Make sure you calculate the endpoints of the budget constraint. b) The price of notepads falls to $1; the price of cafeteria meals remains the same. On the same diagram, draw Emily’s budget line with the new prices and label it BL2. c) Lastly, Emily’s income falls to $90. On the same diagram, draw his budget line with this income and the new prices and label it BL3. Is she worse off, better off, or equally as well off with these new prices and lower income than compared to the original prices and higher income?Suppose the utility function of U(x1, x2) = x11/2x21/2 and the budget constraint of p1x1+p2x2=m. Let’s assume that p1=$1.5, p2=$2, and m=$60. Find the optimal bundle. Also, specify the optimal bundle.
- Mrs. Griffiths earns $5000 a week and spends her entire income on dresses and handbags, since these are the only two items that provide her utility. Furthermore, Mrs. Griffiths insists that for every dress she buys, she must also buy a handbag. Draw an indifference curve showing the optimum choice. Label the optimum as point A. What would be the marginal rate of substitution at the point that corresponds to the optimal consumption choice? Interpret the marginal rate of substitutionDonald derives utility from only two goods, carrots (X) and donuts (Y). His utility 0.1 0.9 function is as follows: U(X,Y) =X Y Donald has an income (M) of $900 and the price of carrots (P,) and donuts (P,) are $45 and $90 respectively Based on this information, what does the slope of the indifference curve for Donald tell us. Select one: A. For each additional quantity of carrot consumed, Donald must give up 0.25 of donuts to maintain the same level of satisfaction B. For each additional quantity of donuts consumed, Donald must give up 1/2 of carrots to maintain the same level of satisfaction C. For each additional quantity of carrot consumed, Donald must give up 1/2 of donuts to maintain the same level of satisfaction D. For each additional quantity of carrot consumed, Donald must give up 1/9 of donuts to maintain the same level of satisfaction E. For each additional quantity of donuts constumed. Donald must give up 1/2 of carrots to maintain the same level of satisfaction. F. For…Cobb-Douglas Preferences] Asad lives in a world with two goods (N=2), apples and bananas. He has a Cobb-Douglas utility function over these goods U(a, b) = a 0.7 b 0.3 . Asad has an income I = 200, and faces prices pa = 2, pb = 1 (a) We know that if Asad is optimizing (and consumes a bundle that contains both apples and bananas), that the slope of the budget constraint should be equal to his MRS. Use this and his budget constraint to solve for his optimal bundle. (b) Suppose the price of apples rises to 4, and the price of bananas rises to 3. What is his new optimal consumption bundle? (c) Suppose Asad instead had a utility function given by U(a, b) = a 1.4 b 0.6 + 1. Given the same prices and income as in part (b), what is his optimal bundle?
- Suppose a consumer has income of 1000, and buys pizza and coke. The price of pizza is 100 and price of coke is 50. Draw a budget line that represents the set of bundles this individual can afford if they use all their income. (Put movies on the X axis). Label the places where the budget line intercepts each axis and the slope of the line. Suppose that in consumer equilibrium this individual consumes 7 pizza and 6 coke. What rules must hold in consumer equilibrium? Label this bundle in your drawing (call it point “A”). Draw an indifference curve associated with this bundle, and explain how its slope at the equilibrium point relates to the slope of the budget line. Consider the bundle 2 pizza and 8 coke. Label this point. What can you say about the slope of the indifference curve that passes through the point? (For example, is it bigger than, equal to, or smaller than -1?) Now suppose that income goes up to 15oo. Illustrate how the budget constraint will change. If both goods are…Suppose your only source of income is work and that you are paid $20 per hour. This determines a budget constraint. You can buy free time at the expense of your income by working less. Likewise, you can get more income at the expense of your free time by working more. Suppose that you can choose how many hours you work. How do you decide exactly on which point of your budget constraint you will choose? Explain this by referring to your indifference curves.Allan is considering his purchase of food (F) and clothing (C). He has utility function UF,C=fc+10f. His income is I=10. He faces a price of food $1 and price of clothing $2. According to this information: 1. Determine the marginal utility of food and clothing, and the budget line of Allan 2. Determine Allan’s optimal basket, and provide a graph indicating that optimal point. Explain your finding
- When plotted Sarah's indifference curve for coffee and tea reveals parallel indifference curves that always have a slope of -1. Suppose that Sarah's budget constraint is 20 -1.5C+1.0T where C is the quantity of coffee and T is tea. If Sarah wants to maximize utility, she will buy: a) equal amount of coffee and tea b) coffee only c) tea only d) more coffee than tea e) a combination of coffee and tea cannot be determined from the information givenSuppose you have a $20 gift card and want to buy Blue and Red yarn. The utility function from yards of blue (B) and red (R) yarn can be expressed as follows: U(B,R) = 3B+R Red yarn costs $4 per yard. blue yarn costs $4 per yard. A) Graph the budget constraint and the indifference curves that can be reached. How many yards of each type of yarn will he purchase at these prices with his gift card?Suppose that the only items you consume are bread and wine. If the price of bread were to increase tomorrow, and if simultaneously your income were to increase by just enough so that you were equally as happy tomorrow as today, what would happen to the level of your consumption of bread ? Illustrate your answer with indifference curves