a. Cosider the functional form F (Kn) K. Which of the as- sumptions 1.1-1.5 in the lecture notes is satisfied by this production func- tion? Explain. b. Show that for the functional form in part a, firms attain zero profit. c. Now consider a more general case of F(K,n), which satisfies the as- gumn or you found

a. Cosider the functional form F (Kn) K. Which of the as- sumptions 1.1-1.5 in the lecture notes is satisfied by this production func- tion? Explain. b. Show that for the functional form in part a, firms attain zero profit. c. Now consider a more general case of F(K,n), which satisfies the as- gumn or you found

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.9P

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Automobile manufacturing is an industry subject to significant economies of scale. Suppose there are four domestic auto manufacturers, but the demand for domestic autos is no more than 2.5 times the quantity produced at the bottom of the long-run average cost curve. What do you expect will happen to the domestic auto industry in the long run?
Break-Even The total revenue function for Frenchdoor refrigerators is given by R = 550x dollars, andthe total cost function for this same product is givenby C = 10,000 + 30x + x2, where C is measured indollars. For both functions, the input x is the numberof refrigerators produced and sold.a. Form the profit function for the refrigerators fromthe two given functions. b. What is the profit when 18 refrigerators areproduced and sold?c. What is the profit when 32 refrigerators areproduced and sold?d. How many refrigerators must be sold to breakeven on this product?
See Hint Suppose you are the owner of a firm producing jelly beans. Your production costs are shown in the table. Jelly Bean Production Вохes Average cost per box 100 $0.95 101 $0.96 102 $0.97 $0.98 103 Initially, you produce 100 boxes of jelly beans per time period. Thena new customer calls and places an additional order for jelly beans, requiring you to increase your output to 101 boxes. She offers you $1.75 for the additional box. Should you produce it? Choose one: O. A Yes, because $1.75 is greater than average total cost, O B. No, because $1.75 is less than average total cost. O C. Yes, because $1.75 is greater than the marginal cost. O D. No, because $1.75 is less than the marginal cost. 9 E. We can't say because we don't know average variable cost.
7. A Managment instutute can operate for a maxium 12 hours .lectures are the outout of the institute and each lecture is for 1 hour abd a mandatory 15 minutes break.If there are F facility abnd C classroom and we consider only threse inputs ,what is the the productiin function of the institute ?How will be production function change if lecture ductation is reduced to 45 mins with a mandatory 15 minutes break
For the firm whose cost curves are shown at right, the minimum efficient scale is OA. about 10 units of production OB. the level of fixed cost corresponding to SRATC₂ OC. about 30 units of production OD. about 50 units of production OE between 30 and 70 units of production. GI Cost per Unit SRATC, SRATC₂ 10 20 SRATC 30 40 50 60 Output per Period 70 SRATC 80 LRAC 90 100
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he total revenue curve of a firm is R(q)=40q−12q and its average cost A(q)=130q−12.85q+20 +400q,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?
10. Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether itproduces any output.a. How does this tax affect the firm’s fixed, marginal, and average costs?b. Now suppose the firm is charged a tax that is proportional to the number of items itproduces. Again, how does this tax affect the firm’s fixed, marginal, and average costs?
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For a firm with a Total Cost function TC C(Q), recall that the definitions of Marginal Cost (MC) and AverageTotal Cost (ATC) are given as follows:Marginal Cost (MC) = C'(0)Average Total Cost (ATC) = C(Q)/QProve that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at itsminimum value.(Hint: By using the definition of average cost function, find the quantity that minimizes it by applying unconstraint optimization.Show that the FOC of the minimization problem implies that MC=ATC has to be satisfied at the minimum level of average cost.)
Refer to the graph shown. If a firm expected to produce 900 units when it built its plant but now desires to reduce its output to 600 units in the short run, it will use the plant size represented by: 0 300 O Multiple Choice O 600 00 SATC₁ Quantity SATC₁. SATC2. SATC3 SATC2 SATC3 SATC₂ SATCA. 900 L 1200 SATC Long-Run Average Cost 1500 Refer to the graph shown. A firm that shifts from SATC₁ to SATC2 is most likely to do so because planned output increases: Cost per unit 0 300 600 SATC₁ Multiple Choice 900 1200 1500 Quantity SATC₂ SATC2 SATC₂ to 300, from 300 to 900. from 300 to 600. SATC Long-Run Average Cost from 600 to 900.