Question

1. To produce cake, you need eggs E and premixed ingredients I. Each cake needs exactly two eggs and one package of ingredients. When you add three eggs to one package of ingredients, you still produce only one cake. Similarly, when you add two packages of ingredients to two eggs, you still produce only one cake. Please CLEARLY write out each step and make sure your handwriting is LEGABLE. Thank you!

   1. Write down the production function that describes the technology of cake production. (5 points)

   2. Draw an isoquant map for this production function. (5 points)

   3. A bird flu outbreak has caused an egg shortage. For the short-run, you are stuck with only

      one dozen eggs. On 3 separate graphs, draw your total product, average product, and marginal product curves. (12 points)

Answer 1

A. Since the production of cake requires eggs and pre-mixed ingredients in a fixed ratio, the production of cake treats these inputs as perfect complements and the production function corresponding to this technology is:$\dpi{80} \fn_phv \small y=min(2E,I)$

B. The isoquants are drawn in the figure below with eggs on the horizontal axis and pre-mixed ingredients on the vertical axis:

C. The new production function is:
$\dpi{80} \fn_phv \small y=min(24,I)$
Total product cannot exceed 24 and is presented in the following graph:

201 -101 OG

Average and marginal product are both constant and equal to one.

20 25 35

The above graph represents both, the average and marginal product.