B: Theory: Cost Minimisation (isocost-lines and production) Note: In the class, I will put capital on the 'Y' axis and labour on the 'X' axis. Obviously, the choice doesn't matter mathematically, but if you want your graph to look like mine, do the same! 3. The wage rate is £10 and the capital rate is £20. If a firm was spending £c, show what combinations of labour and capital are possible in an equation. Represent the combinations possible if the firm spent £200, £400, or £600 in a suitably labelled graph. 4. A firm has technology such that it can produce... q=L+K a. What name do we give to this production function? b. Assume output q = 30. Draw the isoquant in a suitably labelled graph. 5. Assuming the same wages and technology as before - how much does it cost the firm to produce q = 30? How much labour does it employ? How much capital?

B: Theory: Cost Minimisation (isocost-lines and production) Note: In the class, I will put capital on the 'Y' axis and labour on the 'X' axis. Obviously, the choice doesn't matter mathematically, but if you want your graph to look like mine, do the same! 3. The wage rate is £10 and the capital rate is £20. If a firm was spending £c, show what combinations of labour and capital are possible in an equation. Represent the combinations possible if the firm spent £200, £400, or £600 in a suitably labelled graph. 4. A firm has technology such that it can produce... q=L+K a. What name do we give to this production function? b. Assume output q = 30. Draw the isoquant in a suitably labelled graph. 5. Assuming the same wages and technology as before - how much does it cost the firm to produce q = 30? How much labour does it employ? How much capital?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

B: Theory: Cost Minimisation (isocost-lines and production)
Note: In the class, I will put capital on the 'Y' axis and labour on the 'X' axis. Obviously, the choice
doesn't matter mathematically, but if you want your graph to look like mine, do the same!
3. The wage rate is £10 and the capital rate is £20. If a firm was spending £c, show what
combinations of labour and capital are possible in an equation. Represent the combinations
possible if the firm spent £200, £400, or £600 in a suitably labelled graph.
4. A firm has technology such that it can produce... q=L+K
a. What name do we give to this production function?
b. Assume output q = 30. Draw the isoquant in a suitably labelled graph.
5. Assuming the same wages and technology as before - how much does it cost the firm to
produce q = 30? How much labour does it employ? How much capital?

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b. The Yorkshire Cricket Company makes cricket bats out of lumber supplied to it by Acme Sporting Goods, which pays Yorkshire £10 for each finished bat. Yorkshire's only factors of production are lathe operators and a small building with a lathe. The number of bats per day it produces depends on the number of employee-hours per day, as shown in the table below. Number of bats per day 0 5 10 15 20 25 30 35 Number of employee-hours per day 0 1 2 4 7 11 16 22 (i) If the wage is £15 per hour and Yorkshire's daily fixed cost for the lathe and building is £60, what is the profit-maximising quantity of bats? (ii) What would be the profit-maximising number of bats if the firm's fixed cost were not £60 per day but only £30? (iii) How would Yorkshire's profit-maximising level of output be affected if the government imposed a tax of £10 per day on the company? (Hint: This tax independent from the production level.) (iv) What would Yorkshire's profit-maximising level of output be if the government…
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2. Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function Y = K2/6 L3/6 H1/6 a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? (Hint: The marginal product of labor MPL is found by differentiating the production function (Y) with respect to labor (L)) b) Derive an expression for the marginal product of capital. How does an increase in the amount of human capital affect the marginal product of capital? (Hint: The marginal product of capital MPK is found by differentiating the production function (Y) with respect to capital (K)).
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