2 production functions let the production of the iphone 12 be describe

Question

2. Production Functions: Let the production of the IPhone 12 be described by this production function:
Q=100 √KL
Where Q is phones produced, K is capital (measured in machine-hours used) and L is labor (measured in
labor hours).
a. Graph the Q = 2000 isoquant: Set labor to 10, 20, and 40, and find the corresponding values of K. Plot
these values on your isoquant.
b. What can you say about the relative magnitude of rate of technical substitution at L=10 and at L=40?
Is the RTS greater in magnitude at L=10 than at L=40? Lower? The same? Explain. (I'm not asking for
specific values, just the ranking.)
c. Suppose technical progress generates a new production function: Q= 200 √KL
Plot the new Q-2000 isoquant, again solving for K in terms of Land plotting and labeling the K and L
combinations for L = 10, 20, and 40. Describe how this technological change affects the isoquant. (5)
d. Consider a different kind of technological change: suppose that the invention of robots with artificial
intelligence effectively makes capital and labor "perfect substitutes" in the production of IPhones. How
would this technological change affect the shape of the isoquants for IPhone production? How might it
affect the choice of K and L to produce IPhones at any given ratio of wages to capital costs? Explain. (5)
3. Cost curves, profits and losses:
a. Draw short run average cost and marginal cost curves (costs on the vertical axis, q on the horizontal
axis) for a firm characterized by an "efficient scale of production" (so average total cost falls at first as
output increases, and then it rises at high levels of output). Draw these curves so that the minimum
average cost = $6 and is found at q=10. Label everything clearly.
b. Suppose this firm faces a market price for its good of $7, and that it can sell as many units as it wishes
at this price. Add this price to your graph above, illustrate the amount of output the firm will choose to
produce (not a specific value, but just a point in your graph), and identify the area on your graph that
corresponds to the firm's profit at this price.
c. Redraw your graph from part (a), and now suppose the market price is $5. Again, illustrate the level of
output the firm will choose and the area corresponding to the firm's loss at this price.
d. Continuing with the scenario in which the price is $5: Should the firm immediately shut down
production due to its short-run losses, or might it be best for the firm to continue to operate in the short
run? Explain.