Two firms, V E G ( V for short) and Y U M ( Y for short) make Vegemite Suppose firm V has productionfunction qV K 1 4 L 1 4,whilefirm Y hasproductionfunction qY 2 K 1 4 L 1 4 Both firms operate in perfectly competitive Vegemite and input markets, so that they are price takers in both output and input markets Denote the price of Vegemite by p , the price of labor (wage rate) by w and the price of capital (rental rate) by r (a)Whatarethecostfunctionsforthetwofirms (b)Inwhatsenseisonefirmalwaysmoreefficientthananother Whichone (c)Suppose the wage rate is w 1 and the price of capital is r 9 What is the profit maximizing choice of output for the two firms when p 12 (d)Suppose Vegemite is only made by firms V and Y Maintaining the assumption that the firms behave competitively (i e , take the Vegemite price p as given), what is the industry supply curve (e)Suppose firm V acquires firm Y , and so has access to both its own production function as well the production function of firm Y What is its new cost function Will firm V only produce using the most efficient production function Assuming firm V still takes the price of p 12 as given, how much will it produce

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Question: Two firms, V E G ( V for short) and Y U M ( Y for short) make Vegemite. Suppose firm V has productionfunction qV

Two firms, V E G (V for short) and Y U M (Y for short) make Vegemite. Suppose firm V has productionfunctionqV =K1/4L1/4,whilefirmY hasproductionfunctionqY =2K1/4L1/4. Both firms operate in perfectly competitive Vegemite and input markets, so that they are price takers in both output and input markets. Denote the price of Vegemite by p , the price of labor (wage rate) by w and the price of capital (rental rate) by r .

(a)Whatarethecostfunctionsforthetwofirms?
(b)Inwhatsenseisonefirmalwaysmoreefficientthananother?Whichone?
(c)Suppose the wage rate is w = 1 and the price of capital is r = 9. What is the profit maximizing choice of output for the two firms when p = 12?
(d)Suppose Vegemite is only made by firms V and Y . Maintaining the assumption that the firms behave competitively (i.e., take the Vegemite price p as given), what is the industry supply curve?
(e)Suppose firm V acquires firm Y , and so has access to both its own production function as well the production function of firm Y . What is its new cost function? Will firm V only produce using the most efficient production function? Assuming firm V still takes the price of p = 12 as given, how much will it produce?

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