Nir Dagan, Esther Hauk, and Albrecht Ritschl

**Due Monday, June 15, 1998**

**1.** A firm has the production function
`f(x,y)=x ^{1/3}y^{1/3}`

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

**2.**

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