**Production theory**

** **

*Answer the following questions using this week’s required readings (see last lecture slide) and any additional material necessary.*

* *

1. Firm A has a production function of f(x_{1},x_{2})=2x_{1}+3x_{2}. Firm B has the production function g(x_{1},x_{2})=min{2x_{1},x_{2}} while firm C has the production function h(x_{1},x_{2})=x_{1}^{2}x_{2.}

a. What type of returns to scale does each of these firms have?

b. What type of technology are these firms using?

[20 marks]

2. A firm has the following cost function: C(q)=100+q^{2}+3q (where q is the quantity produced).

a. How high are fixed costs for this firm?

b. How high are variable costs?

c. What is the marginal cost of producing one more unit q?

d. What is the firm’s profit function? What is its revenue function?

e. Assume the firm receives $50 per produced good (q), find the cost minimising bundle.

[20 marks]

3. Imagine that a firm has cost given by C(q)=420+3q+4q^{2} and revenue given by R(q)=100q-q^{2}.

a. What is the firm’s profit function?

b. What is the condition for profit maximisation? (How do you make sure that what you found is a maximum, not a minimum?)

c. Calculate the profit maximising bundle.

[15 marks]

4. Imagine that a firm has cost given by C(q)=520+8q+4q^{2} and it receives $200 for every product sold.

a. What is the revenue function?

b. What is the profit function?

c. Calculate the profit maximising bundle.

[15 marks]

5. Now suppose a firm has the production function f(x_{1},x_{2})=x_{1}x_{2}^{2}, the cost for inputs are w_{1}=1 and w_{2}=2 and the price for the produced good is p=10.

a. What are the optimal input levels?

b. What is the optimal output level?

c. What type of returns to scale does the firm have?

[15 marks]

6. Finally, suppose a firm has the production function f(x1,x2)=x13x2, while the cost for inputs are w1=4 and w2=2.

a. What is the marginal rate of technical substitution (MRTS)? Explain its economic significance.

b. What is the profit maximising condition?

c. If the firm wants to minimise costs for an output level of 64 units, what are the cost minimising input levels?

[15 marks]

Subject | General |

Due By (Pacific Time) | 02/10/2015 12:00 pm |

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