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Consider the following demand function:
U(X,Y) = X5Y5
Find the solution of the maximization problem.
Step by step
Solved in 2 steps
- What is the difference between Linear and Non-Linear Demand Function?Jack sells 40 widgets when it charges a price of $40 per widget, and 10 widgets when it charges a price of $100 per widget. Assume the demand for widgets is linear. Write down the inverse demand function of Jack's customers.The demand function for a particular good is x = a + bp. What are the associated direct and indirect utility functions?
- Given the utility function Log Y = 0.42logX1 + 0.58logX2 Find the demand functionthe demand function of a consumer is given as Qd=100-2p. if the demand changes to 100-4p, find the effect of this change on quantity demand at price 10 birrWhat is the sum of the own price elasticity of demand for X, the cross price elasticities, and the income elasticity of demand for X? Does this hold only for the given type of utility function or all well behaved utility functions? What does this mean?
- a. derive the demand function for x1, x2 b. draw the engel curve and demand curve for x2Suppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the quantity of pizza demanded, P is the price of a pizza, and Pb is the price of a burrito. What is the slope of this demand function, and what information does the slope provide?..Consider the demand function for the price of lobster in Maine. Where Qd is the quantity of lobster demanded. (millions of Ibs per year) Pb is the price of butter, Pem is the price of crab meat, and M is the income of consumers. According to the therefore, consumers categorize lobsters as a demand function for lobsters, the income elasticity of lobsters is Qd = 9 – 0.1P – Pb + 0.01Pem + 0.0001M O .278: normal good -280: inferior good -.0001: inferior good O .280: normal good
- Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers (C). Her market research has found that consumer demand for this product can beexpressed as a function of the price of the charger itself (PC), the price of phones (PF), andthe consmer’s income (I). Consumer demand can be described by the function C(PC, PF, I) =(i−10PC)/ (PF) Suppose her chargers come in all different capacities to meet any quantity demanded, so youdon’t need to worry about restricting C to whole numbers for this problem. (a) Does this product satisfy the law of demand?Explain.Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers (C). Her market research has found that consumer demand for this product can beexpressed as a function of the price of the charger itself (PC), the price of phones (PF), andthe consmer’s income (I). Consumer demand can be described by the function C(PC, PF, I) =(i−10PC)/ (PF) Suppose her chargers come in all different capacities to meet any quantity demanded, so youdon’t need to worry about restricting C to whole numbers for this problem. (a) Does this product satisfy the law of demand?Explain. (b) Calculate consumers’ income elasticity as a function of the parameters. (c) Anaya is targeting a market whose income is expected to double over the next five years.Explain whether she should expect the demand for chargers to increase or decrease, andby how much, using the language of normal, inferior, luxury, and necessity goods. (d) Calculate the cross-price elasticity ofCwith respect toPF. (e)…Suppose consumers A and B have the following demand functions for x: For each consumer, is x is a normal good or an inferior good? Explain why.