Mark faces a labor supply decision. His well-behaved preferences over the two goods ‘hours of leisure’...

Mark faces a labor supply decision. His well-behaved preferences over the two goods ‘hours of leisure’ L and ‘consumption’ c can be represented by u = 4 L + c. He has no non-labor income and can choose how many hours to work at the wage rate w per hour. The price per unit of consumption is p, and his available free time is T hours.

a) Sketch Mark’s budget set, with axes, intercepts, and slope labeled (these will depend on the parameters w, p, and T).

b) Use the tangency method to find Mark’s demand functions for leisure and consumption (as functions of w, p, and T).

c) Let’s think about Mark’s “time expansion path” (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T). Sketch it and explain why it has this shape, with reference to Mark’s demand functions.

d) In terms of parameters from the model, what is the most that Mark would be willing to pay to have an extra hour of free time (that is, to increase T by 1)? Why?

Solutions

Expert Solution

Answer:

ekkarill92 answered 1 year ago

Next > < Previous

Related Solutions

Kevin has well-behaved preferences and currently has a bundle with positive amounts of two goods. Let...

Kevin has well-behaved preferences and currently has a bundle with positive amounts of two goods. Let x1 and x2 denote the quantities of goods 1 and 2, respectively. Thinking in terms of x1 on the horizontal axis, the absolute value of Kevin’s marginal rate of substitution between the two goods at his current consumption bundle is greater than 3. Using this information, can the theory we have developed so far predict Kevin’s reaction to the following propositions? (Please show all...

Labor supply. Santi derives utility from the hours of leisure (l) and from the amount of...

Labor supply. Santi derives utility from the hours of leisure (l) and from the amount of goods (c) he consumes. In order to maximize utility, he needs to allocate the 24 hours in the day between leisure hours (l) and work hours (h). Santi has a Cobb-Douglas utility function, u(c, l) = c 2/3 l 1/3 . Assume that all hours not spent working are leisure hours, i.e, h + l = 24. The price of a good is equal...

Consider an economy with two goods, x and y. Explain why if a consumer has well-behaved...

Consider an economy with two goods, x and y. Explain why if a consumer has well-behaved preferences over bundles of x and y then the two goods cannot both be inferior goods. (Please answer that easy to understand)

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences...

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences that can be represented by the following utility function: u(X1, X2) = X1 + X 0.5 2 Let P1 = 4 and P2 = 2. In addition, suppose this individual has an income of $120. (a) Write down the expression for this consumer’s marginal rate of substitution of X1 for X2 (MRS12). Identify the distinguishing feature of this particular MRS12. (b) Calculate the optimal...

1. Consider the preferences of an individual over two goods, x and y, with prices px...

1. Consider the preferences of an individual over two goods, x and y, with prices px and py and income I. (a) If the individual's preferences can be represented by the utility function u(x,y) =2x1/2 + y, what is the marginal rate of substitution? What does this MRS imply about how this consumer would trade y for x? Are the underlying preferences homothetic (explain)? Graphically illustrate a typical indifference curve and explain how you know the shape. (b) If the...

Consider a consumer's preferences over consuming two goods that are represented by the following utility function:...

Consider a consumer's preferences over consuming two goods that are represented by the following utility function: U（x1，x2）= x1^a x2^1-α 0 < α < 1 x1，x2 ≥ 0 (a) Do her preferences satisfy monotonicity? (4 mark) (b) Do her preferences exhibit diminishing marginal utility? (c) Are her preferences convex? In other words, do her preferences exhibit diminishing marginal rate of substitution? (Hint: Find MRS and its rate of changes with respect to the good on the horizontal axis.) (d) Use a...

Consider a consumer with textbook preferences defined over two goods x1 and x2. Why is the...

Consider a consumer with textbook preferences defined over two goods x1 and x2. Why is the condition MRS = p1/p2 necessary for utility maximization? Is this condition alone sufficient?

Consider a consumer with textbook preferences defined over two goods X1 and Y2. Why is the...

Consider a consumer with textbook preferences defined over two goods X1 and Y2. Why is the condition MRS = p1/p2 necessary for utility maximization? Is this condition alone also sufficient?

Jacinto consumer two goods: A and B, his preferences can be represented by the Cobb-Douglas function:...

Jacinto consumer two goods: A and B, his preferences can be represented by the Cobb-Douglas function: U (XA, XB) = 2XA * XB2, where XA represents the units consumed of good A and XB the units consumed of good B. Consider generic prices for the goods PA, PB and an income of m A) Find Jacinto's demand functions for good A and B B) if PA = 60, PB = 90 and m = 540: i. What are the optimal...

Consider a consumer with preferences over two goods (good x and good y) given by u...

Consider a consumer with preferences over two goods (good x and good y) given by u ( x , y ) = x ⋅ y. Given income of I and price of good yas $ P yper pound and price of good xgiven as $ P xper pound, the consumer chooses the optimal consumption bundle given as x ∗ = I 2 P x and y ∗ = I 2 P y . Given P x = $ 1per pound...

Subjects