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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.
In a competitive market, all firms have cost-functions C(y) = y^2 + y + 4. The market demand function is Q = 112-2p. Initially there are 40 firms. (a) What is the market supply function (b) What is the market price and quantity in the short-run
A discriminating monopolist faces the demand schedule Pmkt = 225 - Q and MC = 125 a) What is the market-clearing price for the discriminating monopolist b) How much will the monopolist produce What is the net profits of the monopolist
If your nominal income rose by 5.3 percent and the price level rose by 3.8 percent in some year, by what percentage would your real income (approximately) increase If your nominal income rose by 2.8 percent and your real income rose by 1.1
Bygrave forecasts incremental annual sales revenue of $940,000. Similarly, Bygrave expects total variable costs to increase by $500,000, and total fixed costs to increase by $80,000. Bygrave's marginal tax rate is 39%.
Assume that by investing $2000000 in transportation system we can prevent 30 accidents per year and save another $100 on annual maintenance cost of vehicals using the system ( 2000 vehicles). The annual maintanence cost for this system is $200000.
the daughter of a women with the income in the bottom third of the income distribution will herself have a 60% chance of being in the bottom third, a 25% chance of being in the middle third, and a 15% chance of being in the top third. Income Group..
The income elasticities of demand for movies, dental services, and cloting have been estimated to be +3.4, +1, and +.5, respectively. Interpret these coefficients. What does it mean if an income-elasticity coefficient is negative
Combine your analysis in a. & b. to explain the overall impact on US GDP, and inflation. Use your best judgment about the likely path of adjustment from the initial shock to the long run equilibrium. Show graphically and explain in detail.
Suppose that two firms compete in quantities (Cournot) in a market in which demand is described by P = 260 - 2Q. Each firm incurs no fixed costs but has a constant marginal cost of 20. Suppose that after the cartel is established.
The Human Relations Department of Electronics, Inc., would like to include a dental plan as part of the benefits package. The question is: How much does a typical employee and his or her family spend per year on dental expenses
Suppose that we randomly select a recent graduate of the University of Virginia graduate school of business. This school has a recruiter assessment score of 4.1 and an out- of- state tuition and fees of $ 43,000. Predict the average starting salar..
Consider the Joint Density: 2(x+y) if 0 2. Calculate Fx (0.5) 3. Calculate Fy (0.5)
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