# Problem set 7 of Economic Theory I

Nir Dagan, Esther Hauk, and Albrecht Ritschl

Due Monday, June 8, 1998

1. When the marginal cost is increasing so is the average cost.
2. When the firm may vary all factors of production (inputs), it always produces at the minimum average cost of the short run.
3. 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:

1. The marginal cost curve.
2. The total average cost curve.
3. The variable average cost curve.
4. 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 wx=wy=1.

1. 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.
2. Find the long run cost function and the conditional demands for the inputs.
3. For what quantity of output the short run and long run costs are identical? Draw the graphs of both functions.