Assignment:
1.A firm has the choice of the following investments:
Investment A: costs $5000 today, pays a total of $4000 next year and $1700 the second year. No value beyond that.
Investment B: costs $10000 today, pays $2000 next year and $9800 the second year. No value beyond that
a) Show any calculations used to determine whether the firm will invest in either, neither, or both of these projects if the interest rate is 10%.
b)Repeat part (a) with an interest rate is 5%.
c)Someone claims that the rate of return of project B is 9%. Explain whether or not you can refute this claim base only on the data from parts (a) and (b). Then set up (but do not solve) and equation that would give us an exact answer for the rate of return of the project.
2.An economy is currently made up of a firm that produces bread, a firm that produces butter, and a consumer who consumes both bread and butter. Current production is 100 units of bread, 50 units of butter which the consumed by the consumer. If the output changed to 75 units of bread and 60 units of butter, the profit of the butter firm would go up by $42. The profit of the bread firm would go down by $76. The consumer prefers 75 bread and 60 butter to 100 bread and 50 butter. It is so much better that the consumer would pay $40 more to have 75 bread and 60 butter rather than have 100 bread and 50 butter. Explain, using the definition, why you know it is not Pareto Efficient to have the economy produce 100 bread and 50 butter. (2 points)
3. A demand curve is given by the following equation:
a) Find two points on the demand curve
b) Calculate the Total Revenue from each point
c) Calculate the elasticity between the two points
Explain why the relation between the numbers in (b) and (c) makes sense. (1 point)
4. A firm is a monopolist and faces the following demand:
q P q P
0 148 5 88
1 136 6 76
2 124 7 64
3 112 8 52
4 100 9 40
a) It appears the consumers will continue to pay a positive price if the quantity is greater than 9. Explain why the monopolist will never produce a quantity above 9 no matter what the costs are.
b) For the same demand and the costs given below, find where a profit maximizing monopolist with the demand above will produce and find the profit. Draw a picture of the demand, MR, MC and ATC of the monopolist assuming the good can be produced in continuous quantities. Represent the profit of the monopolist in that graph.
q TC ($) q TC ($)
1 96 6 155
2 105 7 175
3 115 8 200
4 126 9 232