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A consumer has preferences represented by the utility function U(x1, x2) = ln x1 + x2 . Denote prices and income by p1, p2 and I respectively.
a) Write the utility maximization problem and get the first order conditions.
b) Solve the system of equations and find the demand functions (i.e. the optimal choice of x1 and x2 as a function of prices and income).
c) Suppose initially p1 = 10, p2 = 50 and I = 100. What is the optimal choice of x1 and x2? Compute, then draw a graph with the budget constraint and the indifference curve showing the optimal point.
d) Suppose now that the price of good 2 increases, becoming p2 = 120 (still p1 = 10 and I = 100). How does the optimal choice of x1 and x2 change? [Be careful: do you still have an interior solution? can you still use the conditions as in the previous case? how do you compute the optimal x1 now?] How does the MRS compare to the relative price? Compute and show graphically what happens, explaining briefly the economic reason of what you find.
Two alternative investment proposals are under consideration for a vacant owner by Urban Development Corporation. Plan A would require an immediate investment of $120,000 and first-year expenditure for property taxes, maintenance, and insurance of $4..
how should he change his bundle to reach his optimum? Explain your answer using the marginal utility condition at the optimal choice.
OneSource is a producer in a monopoly industry. The demand curve, total revenue curve, marginal revenue curve and total cost curve for OneSource are given as follows: What price will OneSource charge for the output? How much profit will OneSource mak..
In an economy where the equilibrium rate of return on assets is 5 per cent per year, suppose there are three assets A, B and M. A is an acre of land and has an annual cash flow of $50 (received at the end of the year) and is not expected to appreciat..
What is the standard deviation for the class? b. What percentile did you score in?
Your firm's research department has estimated the elasticity of demand for toys to be -0.7. As the manager of the firm, determine the impact of an 8% increase in toy prices on your total revenues.
The University Hall has undergone an extensive remodel that resulted in better premises to purchase and consume food. Students appreciate the remodel and are more likely to spend time at the Hall than before. Food prices after the remodel have increa..
The subway fare in your town has just been increased from a current level of 50 cents to $1.00 per ride. As a result, the transit authority notes a decline in ridership of 30 percent. Compute the price elasticity of demand for subway rides.
Joe and Jim purchase vegetables at a grocery store, but Jim also grows vegetables in his back yard. Only Joe’s grocery store purchases are included in GDP. Only Joe’s and Jim’s grocery store purchases are included in GDP.
A firm has two production processes with the following marginal cost curves:
When supply and demand for a product decreases simultaneously, we can
If both the supply of and the demand for a good are highly elastic, a shift of either curve will always result in. If the supply of rental housing increases causing the price to fall and apartment dwellers move into bigger apartments that cost the sa..
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