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.
Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers (C). Her
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
(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) Anaya expects the price of phones to decrease over the next five years. Explain whethershe should expect the demand for her chargers to increase or decrease using the languageof complements and substitutes. (Note: You don’t need to explain by how much.)
(f) An investor is worried that the price of electricity is increasing. This will make peoplefeel poorer, and therefore will lower the demand for all normal goods including solar-powered chargers. How would you advise Anaya to respond to this concern in economicterms? (Hint: What else matters in addition to the income effect?)
(g) The average customer in the market has an income ofI= 200. If the price of phones isPF= 10, write an expression for the average consumer’s demand curve as a function ofPC.
(h) An investor wants to know how much their investment would benefit customers. Anayanotes that the market price of chargers isPC= 4. What is the consumer surplus to theaverage customer at this price? Show how you calculated this.
(i) One investor tells Anaya she should rethink her calculations because hers would bethe only company selling solar phone chargers in this market. Which perfect-marketassumption is the investor suggesting may be violated? Explain.
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