1. Consider a consumer who consumes two goods. The utility function is given byu(x1, x₂)/2x1+1+√√√x₂,-where x > 0 denotes the amount of good i=the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12.1,2 consumed. Unless stated otherwise,(1) Calculate the marginal rate of substitution (measuring the value of good 1) at theconsumption plan (x₁, x₂) = (3, 4).(2) Calculate the consumption plan that is optimal for the consumer.(3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate itsderivative with respect to p2, i.e., v'(P2), at p2 = 3.(4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demandfor each good.

Consumer maximizes utility subject to the budget constraint. The consumer consumes at the point…

1. Consider a consumer who consumes two goods. The utility function is given by √√2x1 +1+√√x₂, U(X1, X₂) = where x ≥ 0 denotes the amount of good i 1,2 consumed. Unless stated otherwise, the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x1, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its

1. Consider a consumer who consumes two goods. The utility function is given by √√2x1 +1+√√x₂, U(X1, X₂) = where x ≥ 0 denotes the amount of good i 1,2 consumed. Unless stated otherwise, the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x1, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its

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Chapter1: Making Economics Decisions

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Question

1. Consider a consumer who consumes two goods. The utility function is given by
u(x1, x₂)
/2x1+1+√√√x₂,
-
where x > 0 denotes the amount of good i
=
the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12.
1,2 consumed. Unless stated otherwise,
(1) Calculate the marginal rate of substitution (measuring the value of good 1) at the
consumption plan (x₁, x₂) = (3, 4).
(2) Calculate the consumption plan that is optimal for the consumer.
(3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its
derivative with respect to p2, i.e., v'(P2), at p2 = 3.
(4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand
for each good.

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3. The utility that Elena receives by consuming food F and clothing C is given by U(F, C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is £22. MUF = C+1 and MUc = F. (i) Define the term Marginal Rate of Substitution (MRS) (ii) Find the utility maximizing values of C and F for the numerical values given above (Hint: You can assume interior solution). (iii) Now suppose that price of C and Elena's income remain unchanged at £2 per unit and £22, respectively, while the price of F varies. Find the equation of the demand for F as a function of the unit price of F (PF).
Suppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25? PLEASE ONLY ANSWER PART C, D AND E
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
Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.
There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(x, y) = −|4 − x| − |4 − y|where x is the quantity of candy (in grams), y is the quantity of soda (inliters), and |.| denotes the absolute value: for any real number r ∈ R, |r| = r if r ≥ 0 −r if r < 0. The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4, 4), (4, 5), (5, 4), (4, 3), (3, 4), and α(4, 5) + (1 − α)(3, 4) for α ∈ [0, 1]. (b) In an appropriate diagram, illustrate the consumer’s map of indifference curves.
1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5 2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).
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Peter's preferences over two goods, x and y, are represented by the utility function u(x, y) = y + 2x. a) Peter is currently consuming bundle A = (2,4) with 2 units of good x and 4 units of good y. Calculate his current level of utility from consuming this bundle. b) Write the expression the indifference curve representing Peter's current level of utility (i.e., the one you found in part (a). Next draw this indifference curve. c) By looking at the indifference curve you drew in part (b), answer the following questions: Does Peter like good x? Good y? Explain. What can you say about the marginal rate of substitution of good x for y, MRSxy? Is it positive? Negative? Constant? Increasing? Decreasing? Interpret/explain your answer in terms of the tradeoffs Peter is willing to make between goods to keep the same utility level. d) On the same graph you drew in part (b), draw the indifference curve for a utility level of 10. Plot and label in the graph bundles B = (1,2), C = (1,6), and D =…
Please tell me which of the multiple choices in question 1.6)1.7)1.8) are correct.State only the correct ones please. 1.6) The marginal rate of substitution (MRS) can be defined as: Select one or more: a. The amount of one good that the consumer is willing to trade for one unit of the other. b. The ratio of the amounts of two goods. c. The change in the consumer’s utility when one good is substituted for another. d. The absolute value of the slope of the indifference curve. 1.7) (SEE ATTACHED PICTURE) The diagram shows that: Select one or more: a. If Angela works 24 hours a day she can still survive. b. There is a technically feasible allocation where Angela does not work. c. A new technology that produced more grain would give a larger technically feasible set. d. If Angela needed less grain to survive the technically feasible set would be smaller.
Suppose the function for the utility from good c is denoted as U(c)=2c1/2 . Which of the following expressions indicates the marginal utility of c?