[27 points] Allison owns a company which hires labour to produce a good, y. Her income,...
Fantastic news! We've Found the answer you've been seeking!
Transcribed Image Text:
[27 points] Allison owns a company which hires labour to produce a good, y. Her income, I, is given by the profits of the company that she runs. Allison's preferences over lotteries have expected utility representation. Allison is risk averse. Allison has Bernoulli utility function over income u (I) satisfying u' (I) > 0 and u" (I) < 0 for all I. The production function for good y is y = La, where L is labour, y is the output, and 0 < a < 1. Workers are paid the wage w. Allison maximises: max u (pLªwL), L20 where p is the price for the output. Allison is a price taker in both the output market and the input market. [The maximisation problem above says: maximise Allison's utility evaluated at profit equal to (pLawL) by choosing L20. This is not u multiplied by (pLawL). You are not given a functional form for u (I).] (a) Consider the utility maximisation problem for Allison. Solve for the utility- maximising L*. Would the non-negativity constraint bind at the optimal solu- tion? Explain. (5 point) (b) Bob also runs a company to produce this commodity y. Bob faces the same production technology. Bob's preferences over lotteries have expected utility representation. Bob is risk neutral. He has Bernoulli utility function over income u (I) = pLawL. Bob maximises max (pLª-wL) L20 Solve the profit-maximising L* for Bob. (2 points) (c) Compare the answers you obtained in (a) and in (b). How does the risk attitude affect the optimal labour hire? Provide economic and mathematical intuition. (4 points) (d) The price of commodity y is subject to uncertainty. The price p is $10 with probability q and $5 with probability 1- q. Let's first consider the problem of Bob. Bob now maximises expected profits. Set up the maximisation of expected profits by Bob. Derive Bob's first order condition and solve for the profit-maximising level of labour hire. (3 points) (e) Let us now go back to Allison's problem. Allison now faces uncertainty over the price of y as well. As in Bob's case, the price p is $10 with probability q and $5 with probability 1-q. Allison now maximises expected utility. Set up the maximisation of expected utility by Allison. Derive the first order condition. (3 points) (f) Using your economic intuition, discuss whether you expect that the quantity of labour hired by Allison in this case with uncertainty will be the same, smaller, or larger than the quantity hired by Bob (in part (d)). (5 points) Prove formally whether the quantity of labour hired by Allison in this case with uncertainty will be the same, smaller, or larger than the quantity hired by Bob (in part (d)). (5 points) [27 points] Allison owns a company which hires labour to produce a good, y. Her income, I, is given by the profits of the company that she runs. Allison's preferences over lotteries have expected utility representation. Allison is risk averse. Allison has Bernoulli utility function over income u (I) satisfying u' (I) > 0 and u" (I) < 0 for all I. The production function for good y is y = La, where L is labour, y is the output, and 0 < a < 1. Workers are paid the wage w. Allison maximises: max u (pLªwL), L20 where p is the price for the output. Allison is a price taker in both the output market and the input market. [The maximisation problem above says: maximise Allison's utility evaluated at profit equal to (pLawL) by choosing L20. This is not u multiplied by (pLawL). You are not given a functional form for u (I).] (a) Consider the utility maximisation problem for Allison. Solve for the utility- maximising L*. Would the non-negativity constraint bind at the optimal solu- tion? Explain. (5 point) (b) Bob also runs a company to produce this commodity y. Bob faces the same production technology. Bob's preferences over lotteries have expected utility representation. Bob is risk neutral. He has Bernoulli utility function over income u (I) = pLawL. Bob maximises max (pLª-wL) L20 Solve the profit-maximising L* for Bob. (2 points) (c) Compare the answers you obtained in (a) and in (b). How does the risk attitude affect the optimal labour hire? Provide economic and mathematical intuition. (4 points) (d) The price of commodity y is subject to uncertainty. The price p is $10 with probability q and $5 with probability 1- q. Let's first consider the problem of Bob. Bob now maximises expected profits. Set up the maximisation of expected profits by Bob. Derive Bob's first order condition and solve for the profit-maximising level of labour hire. (3 points) (e) Let us now go back to Allison's problem. Allison now faces uncertainty over the price of y as well. As in Bob's case, the price p is $10 with probability q and $5 with probability 1-q. Allison now maximises expected utility. Set up the maximisation of expected utility by Allison. Derive the first order condition. (3 points) (f) Using your economic intuition, discuss whether you expect that the quantity of labour hired by Allison in this case with uncertainty will be the same, smaller, or larger than the quantity hired by Bob (in part (d)). (5 points) Prove formally whether the quantity of labour hired by Allison in this case with uncertainty will be the same, smaller, or larger than the quantity hired by Bob (in part (d)). (5 points)
Expert Answer:
Answer rating: 100% (QA)
a To solve for the utilitymaximizing labor supply we need to maximize the objective function upLa wL subject to the constraint L 0 Taking the derivati... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
The demand for computer monitors is given by the equation Qd = 700 = P, while the supply is given by the equation Qs = 100 = P. In both equations P denotes the market price. Fill in the following...
-
The demand for computer memory chips is given by the equation Qd = 500 - 2P, while the supply is given by the equation Qs = 50 + P. In both equations P denotes the market price. For what price is the...
-
The demand curve for peaches is given by the equation Qd = 100 4P, where P is the price of peaches expressed in cents per pound and Qd is the quantity of peaches demanded (expressed in thousands of...
-
1. Consider the linear system Ax = b (all integer values) with the notation shown below, 1 -3 -1 -2 - H 5 7 - 2261x11 X2 -4 3 9 16x3 615 LX4- = A X b The element a24 = a has been lost. Assume,...
-
Trichloromethane (CHCl3, also called chloroform) has a larger dipole moment than CFCl3. Use three-dimensional structures and bond moments to explain this fact.
-
In supply chain management, what are the differences between agility and adaptability?
-
Use the all-possible-regressions method to select a subset regression model for the Belle Ayr liquefaction data in Table B.5. Evaluate the subset models using the \(C_{p}\) criterion. Justify your...
-
For fiscal year 2011, Starbucks Corporation (SBUX) had total revenues of $11.70 billion, net income of $1.25 billion, total assets of $7.36 billion, and total shareholders equity of $4.38 billion. a....
-
Manufacturing costs for Davenport Company during 2018 were as follows: Beginning Finished Goods, January 1 Beginning Raw Materials, January 1 Beginning Work in Process, January 1 Direct Labor for the...
-
Warf Computers, Inc., was founded 15 years ago by Nick Warf, a computer programmer. The small initial investment to start the company was made by Nick and his friends. Over the years, this same group...
-
Calculate the mug's average initial horizontal and vertical velocities during the preceding time interval. Record in Lab Data to 1 decimal place 1 frame 1 pixel nclination Angle of Surface...
-
Texas Manufacturing has decided to triple the number of distribution centers it operates around North America in order to locate inventories within 500 miles of each major city. What effects should...
-
How do I post this to the ledger the town folk purchased 150 pencils by paying cash totaling $75,000?
-
According to ASU 2020-07, how must contributed nonfinancial assets such as land, buildings, materials, and the use of facilities be presented in a Statement of Activities?
-
Donna Company began operations on June 1. The following transactions took place in June: a. Purchases of merchandise on account were $750,000. b. The cost of freight to receive the inventory was...
-
An accounting department is preparing the year-end warranty accrual. They ask the warranty department to provide past data on the dates, part numbers, and the related repair costs (including both...
-
Consider the following definitions: A function f: RR is called (i) strictly increasing if for any a, b = R such that a < b, we have f(a) < f(b), and (ii) non-decreasing if for any a, b = R such that a
-
Michelles trust is subject to 3.8% surtax on the lesser of the trusts net investment income or the excess of the trusts adjusted gross income over the $12,400 threshold (the highest trust tax rate)....
-
Answer all parts of Problem 3.15 for the utility function U(x, y) = xy + x. The marginal utilities are MUx = y + 1 and MUy = x. In problem 15 a) Is the assumption that more is better satisfied for...
-
There are two firms in an economy. Each of them currently employs positive amounts of two inputs, capital and labor. Their technologies are characterized by diminishing marginal rate of technical...
-
Consider a simple economy that produces two goods, beer (denoted by x) and quiche (denoted by y), using labor and capital (denoted by L and K, respectively) that are supplied by two types of...
-
Distinguish between a direct and an indirect acquisition.
-
What is the acquisition date?
-
Distinguish between a business combination and a non-business acquisition.
Study smarter with the SolutionInn App