Ask Question, Ask an Expert


Ask Microeconomics Expert

problem 1: Joe has the expected utility function u (c1,c2) = p1c10.5 + p2c20.5 where c1 and c2 are consumption levels in states 1 and 2, which occur with probabilities p1 = 3/8 and p2 = 5/8 

a) find out Joe’s expected  utility if c1 = 0 and c2 = 100. find out the expected value of this lottery, and the utility of receiving this expected value with certainty, i.e., of receiving this expected value in both states of nature. Which is larger: the expected utility of the lottery, or the utility of the expected value of the lottery? What does this tell you about  Joe’s attitude toward risk?

b) The certainty equivalent of the lottery is a payoff which, if received with certainty, would make the person indifferent between the lottery and receiving the certainty equivalent in each state. find out the certainty equivalent of the lottery in (a). How does it compare to the expected value?

c) Show that, in general, if one is risk averse, then the certainty equivalent of a lottery falls short of its expected value. The difference between these two is often called the risk premium for the lottery.

d) Find the formula for an indifference curve, giving c2 as a function of c1, identifying combinations of c2 and c1 that give the same expected utility.

e) Find the slope of this indifference curve when c2 = c1. describe why it has this slope.

problem 2: A monopolist has the production function y = z11/2z21/3. Demand is given by p = a - by.

a) Find the conditional input demand for input 1.

b) Find the long-run cost function of the firm.

problem 3: All consumers in a community have the expected utility function

u (c1,c2) = p1c10.5+ p2c20.5. Now c1 = 36 and c2 = 64, which occur with probabilities p1 =1/2 and p2 =1/2

a) Find the expected utility of this lottery.

b) Suppose now there are two agents. Each faces this lottery, but the outcomes are independent. Hence, with probability 1/4 each receives 36, with probability 1/4  each receives 64, and with probability 1/2 , one receives 36 and the other 64. The two agents make an agreement that if one receives 36 and the other 64, the fortunate agent transfers 14 to the unfortunate agent. find out their expected utility under this arrangement. Such an arrangement is the essence of an insurance policy: people facing uncorrelated risks can use the fact that they are unlikely to both experience losses to eliminate some of the risk they face.

c) Suppose again that there are two agents, each facing this lottery, but with perfectly correlated lotteries. Hence, either both receive 36 or both receive 64. Can an arrangement like that of [b] give both agents a higher expected utility than that find outd in [a]?

d) In light of your answers to [a] - [c], describe why it may be easier to insure houses against fires than against floods. What you have just discovered is that if insurance is to be effective, it must involve uncorrelated rather than correlated risks. An insurance policy cannot help with risks that tend to either impose a loss on everyone, or on no one. What risks are likely to fall into this category?

problem 4: A monopolist has a cost function c (y) =100 + ay + by2and faces demand p1 = 100 – y1 and p2 = 150 – 2y2. Define y = y1 +y2.

a) Find the marginal cost function of the firm.
b) Find the profit-maximizing prices in the two markets.
c) Does market 2 affect market 1’s price, and if so, why?
problem 5:

a) John has a von-Neumann-Morgenstern utility function over Bernoulli utility u(c) = c1/2. John has $1000. If John is offered a riskless bond that will pay him $1000 in four years’ time, and the interest rate is r, what price should John be willing to pay for the bond today?

b) Now suppose that the bond is not so riskless. There is a 10% chance that the bond will be worthless when it comes due. What is the most John should be willing to pay?
problem 6: A monopolist has a cost function c (y) =100 + ay. Demand is given by y = 100 – bp(y).

a) The monopolist can perfectly price discriminate (i.e. first-degree). Find the monopoly profits as a function of a and b.

b) Now suppose that there are 10 consumers who each have the demand function y = 100 – bp(y). The monopolist cannot perfectly price discriminate, but can use two-part pricing, setting a fixed fee for access to the good, and then a per-unit price.
Find the optimal fixed fee and the optimal per-unit price.  Find the monopoly profits per consumer as a function of a and b. 

c) What is the consumer surplus per consumer in case (b)?

Microeconomics, Economics

  • Category:- Microeconomics
  • Reference No.:- M91834
  • Price:- $110

Guranteed 48 Hours Delivery, In Price:- $110

Have any Question? 

Related Questions in Microeconomics

Discuss the security issues in addition to simple customs

Discuss the security issues (in addition to simple customs requirements) that your company must consider when transporting customers' goods across international borders. Do the markets your company usually serves make th ...

Discussion questionsanswer both questions 1 and 2 below in

Discussion Questions Answer both questions 1 and 2 below in this same discussion. 1. Research the Microbead-Free Waters Act of 2015 and the Main Street Fairness Act and discuss: • Why do you think the Microbead Act becam ...

How would a low-cost price leader enforce its leadership

How would a low-cost price leader enforce its leadership through implied threats to a rival? How does a firm become a "low cost" price leader? Discuss the specific type of market structure that implied threat strategy ca ...

Discussioneconomic structuralism constructivism and

Discussion "Economic Structuralism, Constructivism, and Feminism" Please respond to the following From the second e-Activity, select the theory that you believe has the explanatory and predictive power regarding the conf ...

Organisation theory multiple perspectivesconcepts you

Organisation Theory: Multiple Perspectives Concepts you should know: a. Communities of Practice b. Social Learning c. Institutionalisation Discussion questions: a. Are the concepts of communities of practice and social l ...

Topic 1 perfectly competitive market structurea perfectly

Topic 1: Perfectly Competitive Market Structure A perfectly competitive market structure has key features. 1. There are many buyers and sellers so neither side of the market has market power. 2. The product provided to t ...

Assignment elasticity of demandin this assignment you will

Assignment: Elasticity of Demand In this Assignment, you will focus on marginal utility, Price Elasticity of Demand, and understanding the difference between Price Elasticity of Demand and Income Elasticity of Demand. We ...

Fight against obesityno unread repliesno

Fight against Obesity No unread replies.No replies. Directions: The impact of obesity is overwhelming and the numbers are staggering in relation to both co-morbidity and cost. Advance practice nurses are in an optimal po ...

Acts of possessioncarefully read acts of possession which

Acts of Possession Carefully read "Acts of Possession," which covers European modes of possessing land and justifying colonization in the Americas. Write a short essay Addressing the following: What common features or as ...

Supply and demand draw curvea define economicsb what do we

Supply and Demand Draw Curve A: Define Economics B: What do we mean by "Scarcity" and how does that relate to the concept of "Opportunity Cost"? C: Distinguish between :macroeconomics" and :microeconomics" D: Distinguish ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate