2. Suppose I have a factory that can produce chocolate chip \& walnut cookies using labor (cooks - l) and capital (ovens - k). My production function happens to be \(40 \mathrm{l}^{.25} \mathrm{k}^{\.5}\). The wage is $5 and the oven rental fee $20. I sell each cookie for $3.

1. The number of ovens is fixed at 2. Graph the production function and an isoprofit line to determine the profit maximizing level of labor. (l on horizontal axis, \(\mathrm{x}\) on vertical)
2. Do I have increasing, decreasing, or constant returns to scale? What is the profit maximizing level of production for the other two types of production functions?
3. Now allowing the number of ovens I can rent to vary, graph the isoquant and isocost curves.
4. Letting the oven rental fee be \(\mathrm{r}\) instead of $20, set up the cost minimization problem graphed in \(\mathrm{C}\).
5. Solve for the optimal amount of labor and capital to be used. Draw the demand curve for ovens as a function of their price when I produce 16 cookies.
6. What do you think happens to the amount of labor used when the price of capital goes up? Illustrate with isoquant & isocost curves. Would this look different if there were increasing returns to scale?
7. Suppose \(r=\) $20 again. Find the equation of the total cost curve when I cost minimize.
8. Graph average cost and marginal cost.
9. Now my business has taken off such that I need to have a food producer's license, which costs $10. What are my short run \& long run supply curves? Will I stay in business in the short & long run with my current cookie price of $3?
10. Mark on the graph the highest \(\mathrm{p}\) at which I produce with no profit, and making a loss in the short run.
11. Suddenly new fuel technology makes heating ovens more efficient. Illustrate how this changes my short run and long run cookie supply curves.

3. Short Answer

1. True or False: It is not possible for a Cobb-Douglas production process to exhibit
   decreasing returns to scale and increasing marginal productivity of one of its inputs.
2. If a firm had everywhere increasing returns to scale, what would happen to its
   profits if prices remained fixed and if it doubled its scale of operation?
3. If a firm had everywhere decreasing returns to scale at all levels of output and it

divided up into two equal-size smaller firms, what would happen to its overall

profits?

Price: $20.17

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