Exercise 1 - A company holds a monopoly for groceries.
Traditionally three different prices have been obtained 1) Western 2) Central and 3) Eastern
P1= 10 -1/20 * x1
P2 = 9 -1/6 * x2
P3= 6-1/2 * x3
x1, x2, x3 are sales measured in 1000 units. The company has incresing returns to scale.
MC(X) = 4 + 1/42x, where x = x1 + x2 + x3 total production.
A) Find the optimal prices for the monopolist.
B) Find an optimal combined price so they all have the same price.
C) Consider if that makes sense.
Exercise 2 - A) There are 100 manufactures of a good each with a cost form of c(x) = 0, 1x + 2x2
Find the supply curve for this good.
B) The good only has one buyer. This buyer uses the good as the only input in production of a consumer good with decreasing returns to scale y= 0, 4√x
Where x is input and y is output. The consumer good is sold at 10 $ each.
Find the buyers demand for this good.
C) Find the monopsonist's marginal expense.
D) Explain that the monopsonist maximizes his profit where the marginal expense and the demand curve intersects. Find optimum and profit.
E) It is considered to split up the production of the consumer good, to a large number of small producers. Expenses will be the same. How much will be produced in this scenario?
Exercise 3 - A hospital - financed by the government - tries to do as many operations as possible, without compromizing the quality of the work done. The government also wishes that as many people as possible are treated, but at the same time the budget remains low.
qλ = b
Let q be the amount that the hospital allocates to quality in each treatment and λ represents the amount of perople treated, b is the budget set by the government.
a) Formulate the game when each part (hospital and government) has utility functions that reflects their preferences as described above.
b) Within this model describe the expected results of the hospital as well as the governments choices.
The quality of the treatment increases with the amount allocated to this, but not proportionally. The achied quality s is measuered on a scale from 0 to 1
s = 1 - e-q
c) What will the result be with respect to 1,b and λ when the hosptials utility can be described as the sum of achied quality pr treatment timed with 90 and the amount of patients treated. The governments utility holds the form √λ + √(100-b)
Exercise 4 - To neighboring countries A & B both holds production of a certain good, only sold domestically. In country A the elasticity of demand is 0,5 and with a price = 16, amount of sales will be 25.
a) Find the demand function.
b) The countries use the same technology, where the variable costs are 1 $ per unit plus an expense for processing that is squared in number of units produced - at 10 units it is 0, 1.
In country A there are 10 manufactures. They all take the market price and chooses their production to maximize profits. Find the supply curve and the market price in country A.
c) In country B the demand is also linear. With price = 16 48 units are sold. If prices decreases with 1$ demands rises with 3. There is only one manufacturer in country B. The marginal costs are 1, 5 no matter the size of the production. Find price and quantity in country B.
d) As a result of economic integration it is now possible to trade cross border. (Costs of transportation are left out and MC is set at 0) Argue how the market will be and find price and quantity.
Exercise 5 - A restaurant in town is known for not wanting to make separate bills for groups, who eat together. After a group has ordered and eaten at the same table in the restaurant, they get a total bill for the whole group. It has been suggested, that the restaurant has chosen this approach because most groups will be tend to share the bill equally so that each person pays the same independently who ordered more or less. And if that is the case, each will single guest be inclined to order more than if the guest got his own bill. Analyze the situation with the following model. There er n guests in a group, each have an utility function of the type ui (xi, mi) = ai lnxi + mi where xi is the quantity of food ordered by a guest, mi is the amount of cash hold by the guest after the visit. The restaurant charges p for each amount of food served. All guests now that they split the bill equally.
a) Compare this to a situation, where each guest pays for his own food.
b) How is the restaurants profit and the guests utility in each of the two cases?
c) Could there be any arrangements that would put the guests in a better situation then these two?
Attachment:- Assignment File.rar