Question 3 The figure shows the housing price (rent) per square foot of houses located at different distances to the employment area (city centre), with and without the consumer substitution effect. Taking point j in the figure as an example, assuming that the household's monthly maximum budget is $800, if the household is living at a distance 10 km to the employment area, the unit commuting cost is $50 per km per month, and the unit price of housing per square foot per month is $0.30. In other words, the household living at point j can afford to live in a 1,000 square feet house, by paying a monthly rent of $300 ($0.30 x 1,000 sf) and a monthly commuting cost of $500 ($50 x 10 km). 3(a) Calculate the maximum house size the household can afford to live at a distance of 5 km to the employment area (point f in the figure).
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- Praxilla, who lived in ancient Greece, derives utility from reading poems and from eating cucumbers. Praxilla gets 30 units of marginal utility from her first poem 27 units of marginal utility from her second poem 24 units of marginal utility from her third poem, and so on, with marginal utility declining by three units for each additional poem. Praxilla gets six units of marginal utility for each of her next three cucumbers consumed, five units of marginal utility for each of her next three cucumbers consumed, four units of marginal utility for each of the following three cucumbers consumed, and so on, with marginal utility declining by one for every three cucumber consumed. A poem costs three bronze coins hut a cucumber costs only one bronze coin. Praxilla has 18 bronze coins. Sketch Praxillas budget set between poems and cucumbers, placing poems on the vertical axis and cucumbers on the horizontal axis. Start off with the choice of zero poems and 18 cucumbers, and calculate the changes in marginal utility of moving along the budget line to the next choice of one poem and 15 cucumbers. Using this step-by-step process based on marginal utility, create a table and identify Praxillas utility—maximizing choice. Compare the marginal utility of the two goods and the relative prices at the optimal choice to see if the expected relationship holds. Hint: Label the table columns: 1) Choice, 2} Marginal Gain from More Poems, 3) Marginal Loss from Fewer Cucumbers, 4) Overall Gain or Loss, 5) Is the previous choice Optimal? Label the table rows: 1) 0 Poems and 18 Cucumbers, 2) 1 Poem and 15 cucumbers, 3) 2 Poems and 12 cucumbers, 4) 3 Poems and 9 Cucumbers, 5) 4 Poems and 6 cucumbers 6) 5 Poems and 3 Cucumbers, 7) 6 Poems and 0 Cucumbers.Ques 1. Sally consumes two goods, X and Y. Her utility function is given by the expression U=3XY2. The marginal utility of X and marginal utility of Y are given by the following equations: MUX=3Y2 and MUY=6XY The current market price for X is $10, while the market price for Y is $5. Sally's current income is $500. A) Draw out Sally’s budget line. (show the points where it meets the vertical and horizontal axes) B) Determine the X,Y combination which maximizes Sally's utility, given her budget constraint. (Partial units for the quantities are possible.) [Hint: One of the ways to do this is to use the equal marginal principle to find the optimal ratio of X to Y and then use that in the budget equation]. C) How much is Sally’s utility? Now the price of X increases to $15. What is the ratio in which she will consume X and Y ?7. Bob receives utility from days spent traveling on vacation domestically (D) and daysspent traveling in a foreign country (F) as given by the utilityU(D; F) = DFThe price of a day spent traveling domestically is 160 pounds and in a foreigncountry 200 pounds. Bobís annual budget for traveling is 8000 pounds. (a) Find Bobís utility maximising choice of days traveling domestically and of daystravelling in a foreign country. Find also his utility level from consuming thatbundle. Suppose that the price of domestic traveling increases to 250 pounds per day.Denoting his budget for traveling x, (suppose by now that it is unknown) findthe demand for D and F under the new prices as a function of x.
- Janie works for an accounting firm. Her wage increased from $30 per hour to $40 per hour. She can work up to 50 hours each week. The table below shows her utility from different levels of leisure and income. Before her raise, if Janie decreases her hours of work from 30 to 20 hours per week, the marginal utility gain from having more leisure is: Hours of Leisure Total Utility from Leisure Income Total Utility from Income 0 0 0 0 10 29 300 40 20 54 400 72 30 75 600 96 40 86 800 108 50 92 900 116 1200 120 1500 122 1600 124 2000 125 Question 4 options: 29 21 13 7Juan is currently working in a job that pays $25 an hour and he chooses to work 8 hours per day. Assume that Juan can work a maximum of 16 hours a day, and he has complete flexibility in how many hours a day he works. Illustrate Juan’s budget constraint and his optimal choice of consumption and leisure. What is the slope of his budget constraint? What does this slope represent? (As on any graph you draw, make sure that you label the axes, the intercepts and the optimal choice.) Juan begins receiving a government transfer payment of $100 per day. Add his new budget constraint to your graph in (a) and show his new optimal choice. Does he choose more or less consumption? More or less leisure? Explain why for both goods. The government imposes a tax of 25% on Juan’s earnings from work and increases his government transfer to $150 per day (the government transfer payment is not taxed.) Redraw the budget constraint from part (b) (omit the part (a) budget constraint), and add a new budget…Suppose Alex’s utility function for appleand orange is U(a, o) = a2o. The price of an apple is $ 4, and the price of an orange is $ 2. Alexhas $ 120 to spend on these two goods.– at the bundle (a, o) = (4, 2) the marginal rate of substitution MRS(a, o) = ____??– Given prices, income, and utility function, the best affordable bundle for Alex is a∗ = __ ??ando∗ = __??
- maddy is a single mom with a weekly budget of $100. She can spend her weeklyincome on food and diapers for her son. Price of food is $1 and price of a diaperis 50 cents. Her son needs at least 5 diapers a day, therefore she must purchaseat least 35 diapers weekly. maddy utility function is U (f, d) = f 0.9d0.1,where f and d represent quantity of food and diapers, respectively.Part aFind Jennifer’s optimal consumption bundle. Make sure to draw her budgetconstraint and indifference curves and clearly demonstrate your solution.Part bmaddy uncle Sam, who is aware of her financial troubles, offers to help herout. Specifically, he offers to pay half of her weekly diaper expenses. Howmany diapers maddy would buy now? Again, demonstrate your solution bothgraphically and analytically.Mika earns $395 per week which she spends entirely at the grocery store, purchasing either food or alcohol. The price of food is $1/unit, while the price of alcohol is $5/unit. If Mika receives an additional $71/week in food stamps that can only be used to buy food at the grocery store (so, this money could be used to buy food but NOT alcohol), what is the slope of Mika's budget constraint at the point where the constraint intersects the vertical axis, were she to graph quantity of food on the horizontal axis and quantity of alcohol on the vertical axis? (Note: The numbers may change between questions, so read carefully).(a) If a consumer has to choose between McDonald burger and King Burger, both are perfect substitute to each other. Explain the conditions of consumer's equilibrium with the help of graph. (b) Suppose that the price of commodity Y is $ 20 per unit while the price of commodity X is $ 15 per unit and suppose that an individual’s money income is $ 100 per period and is all spent on X & Y. Draw the budget constraint line for this consumer at the initial point. If the price of X decreases to $10, incorporate BL2 showing change in the Budget line. Calculate slope of Budget Line for both cases.
- Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? How many dollars will Ricardo choose to save? Check your answers by substituting them into the algebraic statement of the utility‑maximizing rule. In other words, show it works when using this rule.Explain how MRS = MRT is derived for consumers who want to maximize their well-being utility subject to their budget constraint. Also explain how marginal utilities divided by each price of the good are equalized across the available goods is also derived for consumers who want to maximize their being utility subject to their budget constraint.Jamani earns a weekly income of $6000. Suppose he wishes to spend this income on two goods, games and DVDs only. A game costs $200 while a DVDcosts $600. Draw Jamani’s budget line. Putting games on the Y axis. ii. Suppose his income increases to $9000 per week, illustrate what happens to her budget line.iii. Suppose the price of games increase to $600, while his income and the price of DVDs is unchanged from part (i).