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.

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.

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.

Subject | Science |

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

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