Consider the utility function U(x,y) = xy, which describes the enjoyment Emi gets from consumingtacos (x) and sandwiches (y) over a period of 1 week.a) Does Emi like both tacos and sandwiches? Does she like variety?b) Let Emi have budget I=$24, and let prices be Px=$2, Py=$4. Find Emi's optimal basket of goods x andy. Is this an interior or a corner solution?c) What will happen if tacos (good x) go on sale for $1? Find the new optimal bundle.

sider the utility function U(x, y) = xy, which describes the enjoyment Emi gets from consuming s (x) and sandwiches (y) over a period of 1 week. Does Emi like both tacos and sandwiches? Does she like variety? et Emi have budget l=$24, and let prices be Px=$2, Py=$4. Find Emi's optimal basket of goods x and 1. Is this an interior or a corner solution? What will happen if tacos (good x) go on sale for $1? Find the new optimal bundle.

sider the utility function U(x, y) = xy, which describes the enjoyment Emi gets from consuming s (x) and sandwiches (y) over a period of 1 week. Does Emi like both tacos and sandwiches? Does she like variety? et Emi have budget l=$24, and let prices be Px=$2, Py=$4. Find Emi's optimal basket of goods x and 1. Is this an interior or a corner solution? What will happen if tacos (good x) go on sale for $1? Find the new optimal bundle.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q.3. Suppose a student has monthly income of Rs 10,000. He consumes only two commodities Sandwich and Shawarma. The cost of Sandwich is Rs 50 each, and the cost of Shawarma is Rs 100 each.a) Draw the student’s budget constraint. What is the slope of his budget constraint? b) Suppose student gets a raise, so his income increases from Rs 10,000 to Rs 12,000. Show what happens to consumer optimal consumption choice if both Sandwich and Shawarmaare normal goods. Now show what happens if Sandwich is an inferior good.c) Suppose consumer income decreases to Rs. 8,000. Show what happens if both Shawarmaand Sandwich are normal goods. Now show what happens if Sandwich is an inferior good.
Solve these consumer choice problems: a. Suppose a consumer has a utility function u(x, y) = xy + 7y facing prices p,=S1 and p,=$2 and income I = $10. Draw a diagram and find the consumer's optimal consumption of goods x and y. b. Suppose that you are in a situation where you can afford purchasing 3 units of good x and 4 units of good y. You discover that another affordable bundle of 5 units of good x and 2 units of good y causes you to reach the same level of utility. Assume that your utility function and budget line are both well behaved. Are you maximizing your utility by consuming your original bundle? Why or why not? Propose an alternative, affordable bundle that would yield a higher utility level than either of the original bundles.
7. Suppose U = x₁x2 and the budget constraint is given as x₁ + 1 = B, solve for x and 1-α 8. Suppose U = xx and our budget is given as p₁x₁+P2x2 = m, where m is our income. Solve for solve for x and x₂. 9. Suppose now we want to minimize our expenditure while achieving a certain amount of utility. So say our budget is given as P₁x₁ + P2x2, which we want to minimize, while our utility x and x = u, where u is the level of utility we would like to achieve. Solve for x and x₂.
4. Tim wants to maximise his utility given his utility function of U (A, B) = A² B¹. He faces the following prices and income: PA = 25; PB = 20; M = 250. However, a change in the price of good A to PA 22 will change his optimal bundle. If he is only interested in being able to consume his original bundle of goods, how much income would he need after the price change? = (a) Tim would require £54 less income (b) Tim would require £18.33 more income (c) Tim would require £10 less income (d) Tim would require £16.66 more income (e) Tim would require £16.66 less income
II. Your preferences are represented by the utility function U(x₁, x₂) = (x² − x²)0.5 for x₁ > 0, x₂ > 0, and x² > x². 1. Find your marginal utility function for each good.
b. A consumer purchases two goods, the amounts of which are x and y. Her marginal utility of consuming good x is Ux , while that of consuming good ? is Uy. If the two marginal utility functions are given by Ux = y2 + 2xy and Uy = 4xy + 3x2 − 3 and the consumer is known to stay on the same utility curve, find the total utility function of this consumer buying the two goods
refer to question 1 but answer question 2
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2. Utility function: U(X,Y)= 2XY* Budget Constraint: 2X +4Y = 80 a. Calculate the utility maximizing amount of X and Y.
Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…
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