Nir Dagan, Esther Hauk, and Albrecht Ritschl

**Due Monday, June 8, 1998**

**1.** True or false. Explain your answers.

- When the marginal cost is increasing so is the average cost.
- When the firm may vary all factors of production (inputs), it always produces at the minimum average cost of the short run.
- With increasing returns to scale, the tangency between the long run and short run average cost curves occur always at a production level higher then the one in which the short run average cost is at a minimum.

**2.** A firm has the cost function: `c(y)=4+3y ^{2}`.
Find and draw in one diagram:

- The marginal cost curve.
- The total average cost curve.
- The variable average cost curve.
- The average fixed cost curve.

**3.** The production function of a competitive firm is
`Y(L,K)=2L+5K`. If the price of `L` is `w=2` and of `K`
is `r=4`, what is the cheapest way to produce `10` units of output.
Explain your answer.

**4.** A firm has the production function
`f(x,y)=2x ^{a}y^{b}` where

- In the short run the firm employs a fixed quantity of
`y=1`. Find the short run demand for input`x`as a function of the output. - Find the long run cost function and the conditional demands for the inputs.
- For what quantity of output the short run and long run costs are identical? Draw the graphs of both functions.