An aggressive dictator is deciding where to hide his weapon of mass destruction, while the UN is deciding where to look for it. (The US has gotten the dictator to allow UN inspectors to look for it, in exchange for not attacking the dictator’s country.) The payoff to the dictator of successfully hiding the weapon is 5 and from having it found is 2. For the UN, the payoff to finding the weapon is 9 and from not finding it is 4. The dictator can hide it in facility X, Y or Z. The UN inspectors have limited time and personnel, so they can inspect any two facilities –that is, the UN’s pure strategies are XY, XZ, YZ.

a. Write out the normal form game in matrix form, with players 1 = dictator, 2 = UN inspectors.
b. Find a mixed strategy Nash equilibrium.
c. What is the probability that the weapon is found?

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

You are evaluating two different silicon wafer milling machines. the techron i costs $285,000, has a three-year life, and has pretax operating costs of $78,000 per year. the techron ii costs $495,000, has a five-year life, and has pretax operating costs of $45,000 per year. for both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $55,000. if your tax rate is 24 percent and your discount rate is 11 percent, compute the eac for both machines.

In north korea, a farmer’s income is the same as a dentist’s income. in a country with a mixed or market economy, the difference between those two professions might be more than 5 times different. how can you explain the fact that individuals doing the same work in different countries do not earn comparable salaries?