# Problem set 8 of Economic Theory I

Nir Dagan, Esther Hauk, and Albrecht Ritschl

Due Monday, June 15, 1998

1. A firm has the production function f(x,y)=x1/3y1/3

1. Draw isoquants of this production function.
2. Find the firm's (long run) cost function. Draw the firm's AC and MC curves for px=py=10.
3. Find the firm's short run cost function when x2=100. Draw the firm's SAC, SAVC, SAFC, and SMC curves for px=py=10.
4. Find the firm's long run supply function, and draw the supply curve in the drawing of (b) above.
5. Find the firm's short run supply function in the conditions of (c), and draw the supply curve in the drawing of (c) above.
6. How would the answers to (b) and (c) change if the production function were f(x,y)=x2/3y2/3
7. Answer the above questions (a-e) for f(x,y)=[Min{ax,by}]2/3, where a,b are positive constants.

2.

1. Firm A has the short run cost function c(0)=0; c(y)=10+y2, y>0. Find A's short run supply function. Draw the supply curve.
2. Firm B has the (short run) cost function c(y)=20y. Find Firm B's supply function and draw the supply curve.
3. Find the aggregate supply function and draw the the aggregate supply curve.