8. (25 points) With some services (e.g. checking accounts, phone service, or pay TV), aconsumer is offered a choice of two or more payment plans. One can either pay a highentry fee and get a low price per unit of service or pay a low entry fee and a high priceper unit of service. Suppose you have an income of $100. There are two plans. PlanA has an entry fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40with a price of $1 per unit for using the service. Let x be expenditure on other goodsand y be consumption of the service. Explain your answer.(i) Write down the budget equation that you would have after you paid the entry feefor each of the two plans.(ii) If your utility function is u(x, y) = xy, how much y would you choose in eachcase?(iii) Which plan would you prefer? Explain.

The objective of the question is to understand the consumer's choice between two different payment…

Answered: 8. (25 points) With some services (e.g.…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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PROBLEM (1) Suppose a consumer has just enough money to afford the bundle of 3 apples and 2 oranges, and similarly she also has just enough money to afford the bundle of 2 apples and 4 oranges. (a) Denoting the number of apples with x and oranges with y, plot the two given bundles on a graph, and calculate the relative price of apples; px/ py. (b) If she buys only apples with her budget, how many can she buy? If she buys only oranges, how many can she buy? Write down the budget equation for the consumer. (Notice that knowing two points on the budget line, you can write down the budget equation, even though you weren't given the prices nor the income explicitly!) (c) Suppose MUx = 20 and MUY = 30 at some point on the budget line. Is she maximizing utility by choosing this bundle? If not, should she buy fewer apples (and more oranges), or more apples (and fewer oranges), to increase her utility? (d) Forget about (c); instead, you learn that her utility function is u(x,y) = Axy³. What is…
Questions 4 (Choice & Demand). Suppose a consumer's utility function is given by: U(xi, x2 ) = x" a) What is the consumer's demand for x, as a function of income and prices? What is the consumer's demand for x; as a function of income and prices? Use Lagrange method or your intuition. b) What percentage of income does the consumer spend on x;? What percentage of income does the consumer spend on x2?
Note: don't use chat gpt.
3. [30+10] A consumer who consumes two goods and has the following utility function: U(x₁, x₂) = log(x₁ + 1) + log(x2 + 1), where ₁ and ₂ denote the monthly consumption of two goods. The consumer maximizes her utility subject to the following constraints: P₁x1 + P₂x2 ≤m, x₁ ≥ 0, X₂ ≥ 0, where p₁ > 0, p2 > 0 and m > 0. [Hint: Note that log f(x) = f(df (2).] 1_df f(x) dx (a) Write down the Kuhn-Tucker conditions for a point (x₁, x2) to solve the problem, and find all points that satisfy the conditions. Do any of those points solve the problem? (b) Show the above results by drawing indifference curves and budget set on the x₁x2 plane.
(7 points) Suppose Backbeat BBQ, Dave Grohl's one-man catering company, offers two types of membership plans. Plan A has an entry fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40 with a price of $1 per unit for using the service. Let x be expenditure on all other goods and y be the units of consumption of Backbeat BBQ's services, and suppose you have an income of $100. A. Write down the budget equation that you would have after you paid the entry fee for each of the two plans. B. If your utility function is xy, how much y would you choose in each case? C. Which plan would you prefer? Explain.
3. A consumer's indirect utility function is given by V (p, y) = f(p)y. (a) What is the form of this consumer's expenditure function? (b) What kind of preferences does this consumer have?
3. (10 points) 60 50 40 Quantity of Y 30 20 20 B 10 = 11 III A Z M 0 10 20 30 40 50 60 70 80 Quantity of X Suppose that a consumer has the indifference map shown above. The relevant budget line is LZ. The price of good Y is $10. (a) What is the consumer's income? Please show your calculations. (b) What is the price of good X? Please show your calculations. (c) Write the equation for the budget line LZ. (d)) What point in the graph will lead to utility maximizing with the budget line LZ and the indifference curves as shown above? Please label this point as “C” and give an explanation. (e) Please explain why the consumer will not choose point A or point B.
15. Higher Indifference curve means: (a) Consumer has more income (b) Price of goods have reduced (d) All of the above (c) Higher utility level
2. Utility maximization - Trading off labor and leisure The indifference curves on the following graph show Amy's preferences for leisure and consumption for increasing levels of utility, such that her utility increases in both consumption and leisure. Assuming that Amy spends 68 hours each week sleeping, she has a maximum of 100 hours available to her for leisure if she does not work at all. Initially, she works 45 hours (and thus has 55 hours of leisure) and earns $250 per week. Use the grey point (star symbol) to indicate Amy's initial leisure/consumption bundle. Dashed drop lines will automatically extend to both axes. CONSUMPTION (Dollars per week) 1000 900 800 700 600 500 400 300 200 100 0 0 + 10 20 30 40 50 60 70 80 LEISURE (Hours per week) 90 U3 100 110 Initial bundle + $200 Unemployment Benefits Equivalent Bundle, $100 Unemployment Benefits Equivalent Bundle ?
10. (Figure 5.6) Garth spends his income on ice cream and coffee, and coffee sells for $1 a cup. If ice cream sells for $1.50 per gallon, Garth will purchase: Coffee (cups) | 12- 11 10- 9 8- 7- 6- 5- 4 3- 2 34 5678 9 10 Ice cream (gallons) 8 gallons. 6 gallons. 2 gallons. O 1 gallon.
6 (i) FIGURE 6 (i) 22 18 10 1 2 3 Number of video games rented per month 4 All the questions below are referring to Figure 6 (i) and explain and show your computation in your answer. a) The marginal utility of the first video game rental is b) The marginal utility of the third video game rental is c) At which unit of video game, the marginal utility is zero. Total utility
4. Kay lives in a city where housing costs $1 per square foot. They have a monthly budget of$1,000, of which they decide to allocate $500 to rent a 500 sqft. apartment and spend teother $500 on consumption. A generous relative offers Kay a deal on a 400 sqft. apartmentfor only $200 per month, which they accept. What is the equivalent variation of this transferfor Kay, in dollars per month? (Select one)(a) More than $300: Kay gets utility from both consumption and the new apartment.(b) $300: That is how much more Kay can consume with the new cost of rent.(c) $250: That is how much less Kay’s old bundle would have cost at the new prices.(d) Between $0 and $250: Kay would substitute away from her old bundle at the new prices.(e) $200: That is the additional cost of Kay’s new bundle at the old prices.(f) Between $0 and $200: Kay may prefer to substitute away from her new bundle at theold prices.(g) $100: That is the differential cost of the new apartment at the old prices.(h) $0: The new…

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