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Assume a firm wants to minimize its cost of producing y amount using x1 and x2 as inputs, which means it wants to minimize w1x1 + w2x2 subject to x1^(1/2)x2^(1/2)= y:
(a) Using Lagrange multiplier method, find optimal x1 and x2 as functions of w1,w2 and y.
(b) What is the marginal cost of producing a higher level of y?
(c) What is the marginal cost of an increase in w1?
If the industry is regulated and the regulatory authority forces Widget Corp. to earn only a normal return on investment (which is included in its cost function), what is the resulting equilibrium price and quantity. Where W represents the number ..
The following table shows how the total cost of producing canisters of peanuts varies with output and capital in the long run in a perfectly competitive industry. Quantity of Peanut Canisters each hour 0 1 2 3 4 5 6 7 8 Total Cost (K=1) (in dollar..
A basketball manufacturer is considering a number of options for its new factory. Given the following costs and benefits of the four different factory configurations, what are the marginal costs and benefits of the Extra Large configuration
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A Man is planning to retire in 20 years. He can deposit money for his retirement at 6% compounded monthly. It is estimated that the future general inflation rate will be 5% compounded annually. What deposit must be made each month..
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Suppose that you are going to buy a BMW that sells for $40,000. Assume that the interest rate on a savings account is 10% and that your savings account currently has $40,000. For simplicity, assume that BMWs are the only good in the economy.
claimed that if z+x/y, then g(z) = g(x)-g(y), where g(.) represent the growth rate of the variable in question. Prove this result in a formal way using two methods. First, repeat the method that we used in class to prove that if z = xy, then g(z)=g..
On January 1, Frank Jensen bought a used car for $7200 and agreed to pay for it as follows: 1/3 down payment; the balance to be paid in 36 equal monthly payments; the first payment due February 1; an annual interest rate of 9%, compounded monthly.
The total number of movie projections, M, is the sum of the number paid for by each of the two persons: M = MS + ML. Spielberg and Lucas both have income of 70, and the price of both the private good and a movie projection is 1. They are limited, ..
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