doug wants to go into business. For $6000 per month he cn rent a bakery complete
ID: 1099610 • Letter: D
Question
doug wants to go into business. For $6000 per month he cn rent a bakery complete with all the equipment he needs to make a dozen different kinds of donuts (K=1). He must pay unionized donut makers a monthly salary of $1600 each. He projects his production function to be Q=4K (^1/2) L (^1/2) (where Q is tons of donuts). Show computions.
a. Based on the production function, Doug will experience (decreasing/constant/increasing) returns to scale in the (long/short) run. Given this production function, and all other things being equal, we would expect to find (mainly small bakeries/mainly large bakeries/both large and small bakeries).
b. what is Doug's monthly total cost function, as a function of Q? TC = ____ + ____ ____
c. How many bakers will Doug hire to make 20 tons of donuts? ______
d. If Doug produces 20 tons of donuts, what is the marginal cost per ton of donuts?
e. if Doug produces 20 tons of donuts, what is his average variable cost per ton?
f. compute the total product (i.e. tons of donuts) if one worker (_____ tons), two workers (_____ton), and three workers (_____tons), are hired. These numbers would suggest that the marginal product of labor is (increasing/remaining constant/decreasing) as additional workers are hired, and consequently the firms experienceing (diminishing returns / diseconomies of scale) throughout all production levels.
Explanation / Answer
a) Since by doubling the inputs, the output from the production function also increases, Doug will experience constant returns to scale in the long run. Given this production function, and all other things being equal, we would expect to find both large and small bakeries.
b) TC = 6000+ 1600L
Since Q=4K (^1/2) L (^1/2)
Therefore, L = Q^2/16K
Substituting this above,
TC = 6000 + 1000.Q^2
c) Putting Q = 20 and substituting for K = 1 (given) in the production function, one can get L = 25
d) Differentiating the TC function calculated in part (b) with respect to Q and putting Q = 20 will give MC = 4000.
e) Dividing the TVC part of TC function calculated in part (b) by Q, which is 1000.Q^2 and putting Q = 20 will give AC = 20000
f) Substituting values of K = 1 (given) and L = 1,2 and 3 in the production function to get output as:
Q = 4 when L = 1
Q = 5.66 when L = 2
Q = 6.93 when L = 3
These numbers would suggest that the marginal product of labor is decreasing as additional workers are hired, and consequently the firms experienceing diminishing returns throughout all production levels.
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