The budget constraint for a consumer who only buys apples (A) and bananas (B) is PAA + PBB = I where consumer income is I, the price of apples is PA, and the price of bananas is PB. To plot this budget constraint in a figure with apples on the horizontal axis, we should use a budget line represented by what slope-intercept equation?
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- Mrs. Rochester earns $4500 a week and spends her entire income on computers andpastries, since these are the only two items that provide her utility. Furthermore, Mrs.Rochester insists that for every computer she buys, she must also buy a pastry. A) Suppose the price of pastries increases to $20 and income decreases to $3200. Whatis the new algebraic equation for Mrs. Rochester’s budget constraint? Show theimpact of the new budget line relative to the original budget line. B) What would be the new marginal rate of substitution that corresponds to theoptimal consumption choice? Interpret the marginal rate of substitution. D) Assume for this question only that when the price of computers decreases, less ofthat good is demanded. Illustrate the income and substitution effect of this pricedecrease.Robinson Crusoe lives in an island. There are onlytwo food sources in this island: coconut and berries. There is no money in the island but Robinsonuses his time to collect coconuts and berries. He sleeps 8 hours in a day. Collecting a coconut takes2 hours. Picking a pound of berries takes one hour. 1. Considering the food collection times as the prices in the island, write the budget line equationand draw Robinson’s budget line graphically. Specify the intercepts and the slope in the budgetline on the graph.Robinson falls from coconut tree and injures his leg. After the injury collecting coconut takes longer.He can only collect a coconut in 4 hours, but he can still pick berries at the same pace as before. 2. What happens to Robinson’s budget line? Show on the graph. Robinson’s injury makes him more sleepy. Now he sleeps 12 hours in a day. 3. What happens to Robinson’s budget line? Show on the graph.Two weeks after the injury, Robinson’s leg is slightly better, and he sleeps 8 hours…Question 3Draw indifference curves for the following sets of preferences and indicate the direction inwhich the individuals’ satisfaction (or utility) is increasing. Be specific about slopes when itis necessary. Assume for both parts (a) & (b) that soft drinks are measured on x-axis andhamburgers on the y-axis. (a) Mary always gets twice as much satisfaction from an extra hamburger as she does froman extra soft drink. (b) Bob loves soft drinks but dislikes hamburgers.
- 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. What is the algebraic equation for Mrs. Griffiths budget constraint if dresses cost $25 each and handbags cost $14 each? How many of each good will she buy and represent this on a budget line with handbags on the horizontal axis Assume for this question only that when the price of dresses decreases, less of that good is demanded. Illustrate the income and substitution effect of this price decreaseSuppose a consumer has utility function U(X, Y) = X2/3Y1/3. Suppose the consumer has M =$90 to spend and the prices of goods X and Y are PX = $15 and PY = $6 . a. Carefully express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the…Suppose that the quantity of tacos consumed per month is on the x-axis and the quantity of pizzas consumed per month is on the y-axis, a decrease in the price of pizza holding the price of tacos constant will A. cause the budget line to shift inward toward the origin in a parallel fashion. B. cause the y-intercept to remain the same, but the -intercept will move away the origin. C. cause the budget line to shift outward from the origin in a parallel fashion. D. cause the x-intercept to remain the same, but the y-intercept will move away from the origin
- 1. Mary has $100 to spend on goods X and Y. The price of Y is pY = $2.50. Mary has wellbehaved preferences and two of her indifference curves are shown on the above graph along with sometangent points. **This is a graphical problem. You may visually estimate (eyeball) any quantities you need.You may need to locate additional tangencies. a) Suppose the price of X is $1.25. On the graph above, label Mary’s budget line as (BLA) and label Mary’soptimal consumption bundle as bundle A. b) Now suppose the price of X rises to $5. On the graph above, label Mary’s budget line as (BLB) and labelMary’s optimal consumption bundle as bundle B. c) Next find the Hicks Compensated Bundle. To do this, put your ruler on budget line BLB and move yourruler in a parallel fashion until it just touches the indifference curve through bundle A. Label this tangencyas bundle C and draw the line tangent line, along with appropriate || parallel marks, and label this line asthe compensated budget line BLC. Please…Jordan eats two types of fruits – oranges and mangos. He has a budget of $60 to spend on fruits per month. The price of oranges is $4 per bag and that of mangos is $12 per bag. With this information, answer the questions below. Graph Jordan’s budget line by plotting oranges on the horizontal axis and find the slope of his budget line. State the budget equation for Jordan’s consumption of fruits (oranges on the horizontal axis). Suppose the price of oranges has doubled. Show this effect graphically (initial + new budget line) and calculate the slope of the new budget line (oranges on the horizontal axis). Suppose Jordan now reduces the money spent on fruits to $50. Show this budget line change on a graph (oranges on the horizontal axis; price of oranges is $4 and price of mangos is $12). (Suppose a consumer has a monthly income of m = 100 which she spendson two commodities: french fries (x1) and beef jerky (x2). The price offrench fries is p1 = 2 and the price of beef jerky is p2 = 5. (e) What is the slope of the budget line? Provide an economicinterpretation of this number.(f) Because of Mad Cow Disease, the price of beef jerky increasesto $10 (lower supply of beef). On a new graph, plot the originaland new budget constraint clearly identifying how the budgetconstraint has changed. What is the new relative price of beefjerky in terms of french fries?(g) Because of severe shortages, Congress passes the Jerky ReliefAct which limits each consumer to purchase at most 5 packs ofjerky. Show on a graph how this affects the consumer’s budgetset. Answer all three.
- a. Suppose Fiona’s income is $100 per week, which she allocates between chocolates and books. Chocolates cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Fiona might have more than one utility-maximizing solution? b. Confirm that if a consumer’s utility function is described by U = 2X + Y, and prices are px = 2 and py = 1, there is no unique utility maximizing solution regardless of income level. What does this tell you about X and Y as commodities? (Hint: draw a graph showing a budget constraint and indifference curve using the information provided.)Michael can buy either pizzas or submarine sandwiches. If the prices of pizzas and submarine sandwiches double and Michael's money income triples, we can conclude that Michael's budget constraint will; A) shift out but remain parallel to the old one.B) shift in but remain parallel to the old one.C) swivel in so that the slope of the budget constraint is doubled.D) remain unchanged.Take the general case where your income is I, the price of coconuts is Pc and the price of pineapples is Pp. Now—let’s introduce a change. Assume that your income falls, but that the prices of the goods remains the same and answer the questions below: How does this change your budget constraint? Does the slope change? Why or why not? Compare the economic interpretation of the slope in this example with the starting one. Is the consumer able to afford more or less consumption bundles as a result of the decrease in your income? Then we would like you to investigate what happens to the budget constraint if the prices of coconuts and pineapples and your income increase by the same amount—with all other things remaining equal: How does this change your budget constraint? Does it shift or does it rotate? Is the consumer able to afford more or less consumption bundles as a result of the increase in the consumer’s income? In carrying out this activity, please make sure to explain your…
