ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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- Find the elasticity of scale and the elasticity of substitution for the CES production function: 1 1 f(x₁, x₂) = (x³ + x2)³. Solution: We first calculate the marginal products: 2 fx₁ = 3 + = x1fx1 -+ 2 2 10 - ² ( x² + x ) ( + x^²) = ( + + + + ² ) 15 ²0 x² -2/3 x₂ + x2fxz Elasticity of scale = _1₁_+_*__*(+)´<°¸«d«)*;»_ f(x1, f(x1, ‹2)² = -2/3 r2/3 = TRS = t (where TRS = =t). ⇒ r = t³/² ⇒ ln(r) = ln (t) and o = -2/3 dln (r) dln (t) To get elasticity of substitution, we first need TRS and denote r = 1 x3 X1 TMS - F (+4+2)0 = fx₁ fx₂ 2 1 + x²) x₂² MIN x2 3 -2/3 (x² -2/3 2 2/3 2/3 x1 -2/3 = r²/3 x¹/3 + 1/3 = 1.arrow_forwardWorldwide quarterly sales of a brand of cell phones were approximately q = −p + 156 million phones when the wholesale price was $p. (a) If the cellphone company was prepared to supply q = 4p − 384 million phones per quarter at a wholesale price of $p, what would have been the equilibrium price? $ (b) The actual wholesale price was $103 in the fourth quarter of 2004. Estimate the projected shortage or surplus at that price. There is an estimated ______ of million phones.arrow_forwardIn one month, a Pizza Hut restaurant sold 5500 personal pizza at RO 4.50 per pizza. When this restaurant increased its price by 30%, its total revenue for the next month increased to RO 18,720. As a result of this price increase, however, the monthly sales of POP decreased from 3500 to 3000 cans. Using the arc elasticity method: (i) Find the own price elasticity of demand for this restaurant’s pizza. (ii) Find the cross elasticity of demand for pop with respect to the price of the pizzas. Are the two substitutes or compliments?arrow_forward
- 15arrow_forwardWorldwide annual sales on smart phones over a two year period were approximately q=-5p+3090 million phones at the selling price of $p per phone. (a) obtain a formula for the price elasticity of demand E. E=______ (b) in one of the years the actual selling price was $355 per phone. What was the corresponding price elasticity of demand? E=______ The demand is going (up/down) by about _____% per 1% increase in that price level.arrow_forwardQ3. Refer to the diagram. Using the midpoint formula, calculate the price elasticity of demand between the prices of $15 and $12. Accordingly, state whether demand is elastic or inelastic between these two points. P$/unit 15 12 D 18 22 Q (units/week) Ep = Damand ie ... Q4. For each case below, answer the bolded questio Classification of the Case Calculations product(s) if requested to do so 1. Suppose that a 2% increase in income in the economy decreases the quantity of gadgets demanded by 1% ar every E,= Gadgets are possible price. Find the income elasticity of demand and dassify the product accordingly (state whether gadgets is a normal, necessity, luxury or an inferior product). 2. A firm finds that its price elasticity of demand is 4.0. Currently, the firm is selling 2000 units per month at $5 per unit. Price must be lowered by= If it wishes to increases its quantity sold by 10%, by how much it must lower its price? 1 Suppose legalization-and subseque nt regulation-of products Xand…arrow_forward
- PRICE (Delars per tor 18 24 M 4 12 24 QUANTITY (Thousands of tons) Supply Demand O Total Revenue (Thousands of Dollars) Demand Supply Several growers are happy with this advancement in technology because now they can sell more crops, which they believe will lead to increases in revenue. Using elasticities, you will be able to determine whether this price change will lead to a rise or fall in total revenue in this market. Using the midpoint method, the price elasticity of demand for pistachios between the price levels of $15 and 59 per ton is 0.33, meaning that between these two points, demand is inelastic. Thus, you can conclude that the grower's claim is incorrect because total revenue will increase due to the technological improvement. Confirm your previous conclusion by calculating total revenue in the pistachio market before and after the technological improvement. Enter these values in the following table. Before Technological Improvement After Technological Improvementarrow_forwardNote:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.arrow_forwardNumbers 5 adn 6 need to be answered. The function (8.6) needed in 5b has been included in a separate picture. Please show all work. Thank you.arrow_forward
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