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Explain the technique of constrained optimization in relation to utility functions and how it relates to consumer equilibrium.
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- Assume that U(X, Y) = Xa Yb Budget constraint is I = Px X + Py Y Please solve the above utility maximization problem (constrained optimization) using Lagrangian Method for the optimal quantities X* and Y* showing step-by-step solution.suppose a firm's objective is to maximise its output in a given constraint for expenditure.?discuss least cost combination for this objective of the firm?The demand for monorail service in a city in 2005 can be approximated by q = −4,500p + 41,700 rides per day when the fare was $p. Find the function R for total daily revenue in dollars, in terms of p only, subject to any constraints. R(p) = Find R′(p). R′(p) = What price (in dollars) should have been charged to maximize total daily revenue? (Round your answer to the nearest cent.) p = $
- Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F) = 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $4000. Suppose F is on the horizontal axis and D is on the vertical axis. Jane's marginal rate of substitution between F and D is equal to 10 1 F/D D/Fa hicksian demand is found by minimizing cost subject to a budget constraint. is it true or false?You have k20 per week to spend and two possible uses for the money: telephoning friends back home and drinking coffee. Each Hour of phoning costs k2 and each cup of coffee costs k1. Your utility function is U(X,Y)=XY,where X is the hours of phoning you do and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility levels? You can use the standard result on the constrained maximization of such a function, but must state in clearly
- There is no demand for a certain make of one-time use camera when the unit price is $ 12. However, when the unit price is $ 8, the quantity demanded is 8000/week. The supplier will not market any cameras if the unit price is $ 2 or lower. At $ 4/camera, however, the manufacturer will make available 5000 cameras/week. Given that both the supply and demand equations are linear: Determine the associated linear demand function Determine the linear supply function. At what price should the camera be sold so that there is neither a surplus nor a shortage?A company that makes sweatshirts is willing to supply 156 sweatshirts each month if the price is $24 each and will supply 204 sweatshirts each month if the price is $36 each. Find the linear supply function, qS where qS is the number of sweatshirts the company is willing to make available per month at a price of p dollars per sweatshirt. A.qS = 12p + 48 B.qS = p/12 – 48 C.qS = 0.25p – 15 D.qS = 4p + 60You have £20 per week to spend, and two possible uses for this money: telephoning friends back home, and drinking coffee. Each hour of phoning costs £2, and each cup of coffee costs £1. Your utility function is U(X,Y) = XY, where X is the hours of phoning you do, and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility level? You can use the standard result on the constrained maximization of such a function, but must state it clearly. Now suppose the price of telephone calls drops to £1 per hour. What are your optimal choices? What is the resulting utility level? How much income per week will enable you to achieve the same quantities at the new prices as the ones you chose before? What income will enable you to attain the same utility as you did before? Comment on your answer in the context of equivalent variation and compensating variation.
- Discuss what is Market Pricing and identify all salient factors of market pricing on economic decision-making.The estimated monthly U.S. demand function for avocados isQ = 144 − 40p + 20pt where p is the price of avocados and pt is the price of tomatoes, a substitute for avocados. The estmated supply function is Q = 58 + 15p − 20pf where the price of fertilizer, pf , is $0.40, so the supply function can be written asQ = 50 + 15p. The initial price of tomatoes is $0.80 per lb. Using algebra, determine the initial equilibrium price and quantity of avocados, and then determine how price and quantity change if the price of tomatoes increases by $0.55 to $1.35The demand function for a truckload of firewood for college students in a small town is QC = 400 − p. It is sometimes convenient to rewrite a demand function with price on the left side. We refer to such a relationship as the inverse demand function. Therefore, the inverse demand function for college students is p = 400 − Qc. The demand function for other town residents isQr = 400 − 2p. 1. What is the inverse demand function for other town residents? 2. At a price of $300, will college students buy firewood? What about other town residents? At what price is the quantity demanded by other town residents zero? 3. Draw the total demand curve, which sums the demand curves for college students and other residents.
