EBK MICROECONOMICS
2nd Edition
ISBN: 9780100254138
Author: BERNHEIM
Publisher: YUZU
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Chapter 3, Problem 6CP
(a)
To determine
Constraint optimization function.
(b)
To determine
Best choice.
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This question illustrates the argument on p.114 of the book.
A and B own neighboring properties. Beneath their properties is a common well that contains 200 units of oil. The cost to A of extracting oil from the well in period t depends on the number of units of oil in the well at the beginning of the period t, ut, and the number of units of oil A extracts in period t, xAt ; specifically, the average cost of extraction for A per unit in period t is xAt /ut. The analogous cost function for B is xBt/ut. The market price of a barrel of oil is 1, there are two periods (t = 1, 2), and the discount rate is zero. The oil is a common property resource.
a) (2) Suppose that A and B "unitize" and cooperatively decide how much oil to extract, and split the profit between them. The jointly profit-maximizing policy is that each extracts 50 units of oil from her well in each of the first two periods, after which the well is dry. How much discounted profit will A and B each make?
b) (2) Suppose…
Your firm specializes in recycling used plastics into consumer goods. You have three production opportunities:
1. You can produce plastic utensils for a revenue of $30,000 while production will cost $15,000.
2. Alternatively, you can produce lampshades: you calculate that at the optimal production, you expect to sell 2,000 lampshades every year at $10 each, and your average total cost per lampshade will be $2.
3. You also have the option to shut down your factory and produce nothing at a cost of $1,000 a year.
Which opportunity do you choose?
4 Instead of working hard, Kendall Square Inc’s manager can shirk and not improve costs. In order to incentivize her hard work, Kendall Square Inc’s shareholders want to give the manager a bonus if they see that variable costs are cut by half.
What is the maximum bonus that shareholders would be willing to give?
A small bank is trying to determine the number of tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributed. If the delay cost per customer day is $200, how many tellers should the bank hire?
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- 1. Inputs K, L, R and M cost £10, £6, £15 and £3 respectively per unit. What is the cheapest way of producing an output of 900 units if a firm operates with the production function Q = 20K0.4L0.3R0.2M0.25? 2. Make up your own constrained optimization problem for an objective function with three variables and solve it. 3. A firm faces the production function Q = 50K0.5L0.2R0.25 and is required to produce an output level of 1,913 units. What is the cheapest way of doing this if the per-unit costs of inputs K, L and R are £80, £24 and £45 respectively?arrow_forwardIt is known that a certain company sells each kg of the product it manufactures at $80, it is also known that the total manufacturing cost "CT" is given by the function CT=(1/1000)x2 +100 , where "x" are the kg of product produced. a) How many units of "x" must the company sell to break even? Value = 100 points.b) How many units of "x" is the optimal quantity that should be sold to optimize the producer's profit? Value = 100 points.c) How many monetary units does that optimal profit for producers amount to? (remember, you will have to prove it mathematically either by the method of the first or by the method of the second derivative). Value = 100 points.arrow_forwardSuppose the input combination currently used by a producer is such that the TRS is equal (in absolute value) to the ratio of the input prices. Then, we can conclude that the producer is maximizing her profits. Group of answer choices True Falsearrow_forward
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