1. Corruption

There are 2 firms competing for an oil lease that will give a payoff of $100. The larger the bribe a firm gives to the government, the higher the probability of getting the oil lease. The probability, pi, of getting the lease for firm i, is their bribe, xi, divided by the total bribes of both firms: x1 + x2.

So, pi = xi / (x1 + x2) [and in general with n firms, pi = xi / (x1 + x2 + ... + xn) ] Expected profits for firm i are then: pi(100-xi) + (1-pi)(-xi).

The bribes in equilibrium will be 100(n-1)/n = nx = total bribes paid to the government, where n is the number of firms, so with 2 firms, each firm will pay a bribe of 25.

a. What is the expected profit of each firm?

b. Another firm is thinking about entering the oil market and making its own bribe. What is

the expected profit of firm 3 of entering the market? What is the expected loss of profit of

each of the initial two firms?

c. If the first two firms could prevent firm 3's entry by collectively paying firm 3 to not

enter the market (they would have to pay a combined amount higher than firm 3's profits from entry that you found in part b.), would it be worth it for the two firms to pay firm 3 to stay out of the market?

2. Agricultural Household Model

a. Assume there is a farming household which has to make a decision about how much food to produce. The marginal cost of producing an extra unit of food, where Q is the total quantity of food produced, is MC = 0.5*Q. If the price of food, PFood, = $10, how much will the farm produce? What is the farm's profit?

b. The price of other stuff is POther = $5. Assume the household has consumption preferences such that the household utility = minimum of (XFood, XOther), where XFood is the amount of food consumed and XOther is the amount of other stuff consumed. That is if XFood = 5 and XOther = 10, the household's utility is 5. If XFood = 5 and XOther = 100, the household's utility is still 5. (These are called Leontief Preferences.)

First, draw the budget curve for the household, assuming that all of its profits from part (a) are exactly equal to its income. Put the amount consumed of other stuff on the Y-axis and food on the X-axis. Second, determine the amount of food (XFood) and other stuff (XOther) that the household consumes given the household's utility function. (The household can buy fractions of the goods, e.g. if it has $2, it can buy 1/5 of a unit of food.) Hint: It may help to draw some indifference curves and trace out the path they take.

c. Assume the price of food increase to PFood = $12. What is the new amount of food that the farm household produces and what is the farm's profit?

d. Assume the price of other goods is unchanged. Draw the new budget constraint for the household and find the new consumption level of the household for food and other goods. Does the amount of food consumed go up or down? Comparing the situation where PFood = $10 vs PFood = $12, how much net food is produced for the market, that is, what is total amount of food produced minus amount of food consumed in each case? Why might it be difficult to use food price increases to get farm households like this one to increase food production for non-farm households to purchase?