Consider a consumer with an income of M = 200 in an economy with 3 goods. Let the prices be p1 = 4, p2 = 2 and p3= 21, respectively. a. Define the budget set facing the consumer. b. Find two bundles, (x1, x2, x3) and (y1, y2, y3) that the consumer can afford. Can the consumer afford the average of the two bundles in your example? Why or why not? c. Suppose the price of good 3 decreases to p3= 15. Can the consumer afford the two bundles you described before now? Why?
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- Assume that the data in the following table are an indifference curve for a consumer: a. graph this indifference curve and label "Quantity of Y" on the vertical axis and Quantity of X" on the horizontal axis. Label the points A-D. b. Assume the consumer's budget is $12 and the price of X and Y are $1.00 and $1.50, respectively. Draw the budget line in the above graph. c. what combination of X and Y will the consumer purchase? d. What is the value of the MRS and the slope (Px/Py) at consumer equilibrium? e. Beginning with the graph drawn in part (a), explain and draw graphs to derive demand curve for X Choice units y units of x A 10 2 B 6 4 C 4 6 D 2 12A consumer consumes pizza and soda always in the fixed proportion of 3 slices of pizza (x) with 2 cups of soda (y). Any pizza or soda not consumed together with the proportional amount of the other is useless to her. (a) Write down a utility function u(x,y) that represents her preferences. (b) If she has I = $60 budget and px = 4, py = 4, what is her optimal bundle? (c) In (b), If the price of soda increases to $6, how much money should she be compensated so that she achieves the same level of utility before the price increase? (d) Returning to (b), If the price of soda increases to $6, how much should the price of pizza be reduced so that she achieves the same level of utility before the price hike? (e) In (a), what values of a and b she is indifferent between the bundle "30 slices of pizza and a cups of soda" and the bundle "b slices of pizza and 40 cups of soda". Find at least two (a,b) pairs to get full points.Carol needs to decide how to spend her wealth on fish and chicken. For Carol, 1 lb of fish is equivalent to 2 lb of chicken. Her preferences can be represented by the utility function u(x; y) = 2x + y where x is the quantity of fish (in lbs) and y is the quantity of chicken (in lbs). The consumption set is R2+. a) Suppose now that the price of fish increases to $2 per pound. Draw Carol's budget set, labeling the slope and the intercept points clearly. How much fish and chicken will Carol choose to purchase? b) Suppose that Carol goes to a different supermarket where the price of fish is Px > 0 (in dollars per pound of fish) and the price of chicken is Py > 0 (in dollars per pound of chicken). Find Carol's demand for fish as a function of the prices Px and Py . You can assume that she still has $20 to spend. Assume that the price of chicken is Py = 1. Draw Carol's demand function for fish as a function of the price of fish (Px) in a diagram with the quantity of fish on the…
- Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S + T) = 2ST, so Mus = 2T and Mut = 2S. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on shoes and dancing What is the equation for her budget line? Draw it (with T on the vertical axis), and label the slope and intercepts. What is Linda’s marginal rate of substitution? Explain. Use math to solve for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget lineAnswer the question on the basis of the following two schedules, which show the amounts of additional satisfaction (marginal utility) that a consumer would get from successive quantities of products G and H. Units of G MUG Units of H MUH 1 36 1 70 2 33 2 60 3 27 3 55 4 21 4 45 5 18 5 30 6 12 6 25 7 6 7 15 If the consumer has a budget of $29 and the prices of G and H are $3 and $5, respectively, the consumer will maximize their utility by purchasing Multiple Choice 3 units of G and 4 units of H. 4 units of G and 2 units of H. 1 units of G and 5 units of H. 2 units of G and 5 units of H.Suppose a consumer’s preferences can be represented by the utility function U(X,Y) = Min (2X,Y). Also, suppose the consumer has $300 to spend and the price of Good X is PX = $2 and the price of Good Y is PY = $5. If the consumer maximizes their utility subject to their budget constraint, how much of Good X and how much of Good Y will the consumer purchase? X* = Y* =.
- I need help with this homeowrk question i am unsure if i have it correct. Suppose a consumer’s utility function is given by U(X,Y) = X^1/2*Y^1/2. Also, the consumer has $36 to spend, and the price of good X is P(x) = $4. Let good Y be a “composite” good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X.if P(x) increases to 9 and the new bundle of the customers demands are 2 units of x and 18 units of y, how much additional money would the consumer need in order to have the same utility level after the price change as before the price change? (Note: this amount of additional money is called the Compensating Variation.) and of the total change in the quantity demanded of good X, how much is due to the substitution effect and how much is due to the income effect? (Note: since there is an increase in the price of good X, these values will be…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.Suppose that the consumer maximizes his utilitysuch that the marginal utilities of goods X and Y are; MUx=80-16x MUy=60-2y Let Px=P4,Py=P2 and I=P80 Find the utility maximizing quantities X and Y
- Ursula views one cup of frozen yogurt to be a perfect substitute for threepieces of chocolate chip brownies. A cup of frozen yogurt sells for $6, and a piece of chocolate chip brownies is $3, and Ursula has a monthly budget of $180 to buy frozen yogurt andbrownies.a) What bundle should Ursula buy to maximize her utility? Show how to determine this bundle on a diagram using indifference curves and a budget line ((with frozen yogurt –Y– on the vertical axis).b) If the price of a cup of frozen yogurt increases to $9, how would Ursula’s behavior change? Show the utility-maximizing bundles on diagrams with budget line and indifference curves (with frozen yogurt –Y– on the vertical axis).Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S,T) = 2ST, so MUs = 2T and MUT = 2S. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on shoes and dancing. A. What is the equation for her budget line? Draw it (with T on the vertical axis) and label the slope and intercepts. B. What is Linda's marginal rate of substitution? Explain. C. Use math to solve for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget line.