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Suppose that a consumer=s preferences over two goods, x and y, are represented by a Cobb-Douglas utility function:
U(x,y) = x1-β yβ
a. Find the expenditure function of the consumer, and the compensated demand functions.
b. Suppose that β = 1/4 and that initially a consumer is in equilibrium with px = 1, py = 1, I = 100. What are the demands for x and y.
c. Starting from the position in part b, the price of good y rises to 2. What is the increase in the "consumer price index" (CPI) for this consumer?
d. What is the minimum increase in income necessary for the consumer to be as well off under price px = 1, py = 2, as she/he was at prices px = 1, py = 1? Explain why the percentage increase is smaller than the increase in the CPI for the consumer that you derived in part c.
Consider a committee that consists of three people, A, B, and C, that is to examine three proposals, x, y, and z. The committee can adopt at most one of the three proposals; it also has the option of adopting none.
The production function for product y is given by y = min {l; 2k}. The price of capital is r = 120 per day and the price of labour is w = 30 per day. Determine the (daily) total cost C(y) and marginal cost MC(y) of manufacturing this product.
On the basis of the information regarding the risk involved in the two projects, you come up with the following probability distributions for the projects:
Assume an economy with 1000 consumers. Each consumer has income in the current period of 50 units and future income of 60 units and pays a lump-sum tax of 10 in the current period and 20 units in the future period.
The following function describes the demand condition for a company that makes caps featuring names of college and professional teams in a variety of sports. Q = 2,000 - 100 P where Q is cap sales and P is price. a) How many caps could be sold at $..
The many identical residents of whoville love drinking zlurp. Each resident has the following willingness to pay for the tasty refreshment: first bottle-$5 second bottle-$4 third bottle-$3 fourth bottle-$2 fifth bottle-$1 further bottles-$0.
A bank has $120 million in total assets, which are composed of reserves, loans, and securities. its only liabilities are $120 million in transactions deposits. The bank exactly satisfies its reserve requirement, and its total reserves equal $6 mil..
Give a numerical example to show that a monopolist's marginal revenue can be upward sloping over part of its range. Hint: The price on the demand curve is the producer's average revenue. Think of a graphic that shows the possibility of declining a..
The economy of Sonrisa has 1000 people in three income categories: poor, middle class, and rich. The poor ear $500 per year and have to spend it all to meet their consumption needs. The middle class earn $2,000 per year, of which $1,500 is spent a..
Each of 100 rms in a competitive market has a cost function of c(Q) = 72 + 2Q2, meaning each rm has a marginal cost of MC = 4Q. The market demand curve is QD = 600 5p. a. Solve for the short-run equilibrium price and quantity
In his current job, Smith can work as many hours per day as he chooses, and he will be paid $1/hr for the first 8 hours he works, $2.50/hr for each hour over 8. Faced with this payment schedule, Smith chooses to work 12 hr/day.
The Texas Family Assistance Program (a social welfare program) offers cash transfers to low-income families. Suppose that the maximum transfer is $20 for households without income; for each dollar earned, the transfer is reduced by $0.50.
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