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+3y2.
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)=2xayb where a=1/4 and
b=3/4. The prices of the production factors (inputs) are
- 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.