# (solution) Hi Can you help me to answer number 1 to number 3, it is due in 2

ECON 2020: A
Intermediate Microeconomics I: Production
Problem Set # 1
Department of Economics, Carleton University
Fall 2016
Due Date: September 27, 2016 In this problem set, as in all following ones and the exams, the term marginal refers to
an infinitesimally small increment. In other words, use derivatives to determine
marginal products etc. 1 Short-run production (6 points) Pepsi Inc. produces soft drinks in quantity q in a manufacturing plant in Canada with labor input
L and capital K according to the production function
1 = (, ) = 7 + (3?2) 2 2 ? 3
3 In the short run, no additional capital can be used, but workers can work overtime, so that
labor input is flexible.
(a) What is the short-run marginal and average product of labor for a given capital stock K? (2)
(b) For the following, assume that K = 4. For which value of L do the functions MPL and APL
intersect? What is the maximum of the APL function? What is the connection? (2)
(c) Where does the production function stop to be defined? What is the reason? (1)
(d) Does the law of diminishing marginal returns hold? Why? [One sentence is sufficient.] (1) 2 Long-run production (6 points)
Another firm in the same industry, Coke, considers setting up a plant in Canada and is thus
evaluating its long-run production possibilities there. Besides using machinery K, it can hire labor
L. The production function is = (, ) = 1?2 1?2
(a) What is the equation of the isoquant, i.e. K as a function of L (and output)? (2) 1 (b) What is the marginal rate of technical substitution? (2)
(c) The manufacturer estimates that it will sell 12 units of its product. How many additional units
of capital do you need to substitute for one marginal unit of labor when L = 6? How many do
you need when you want to substitute for one marginal unit of labor when L = 12? In which
case do you need more additional capital?1 (2) 3 Production (6 points) The firm Avanti produces custom-made sports cars that appeal to a certain clientele because of
their high price and thus exclusivity. Avanti has the following production function:
(, ) = 2?3 1?3 where k and l are the capital and labor input respectively.
(a) What additional output does one additional marginal unit of capital produce when the capitallabor ratio is (k/l) = 8? (2)
(b) If Avanti employs one marginal worker less, how many additional units of capital does the
firm need to produce the same output? Again, assume that the capital-labor ratio is (k/l) =
8. [Do not assume this any further.] (2)
(c) How many units of labor does the firm need to produce q units of output in the short run when
the capital stock is fixed at a level of k = 5? (2) 4 Multiple-choice question (2 points)
With increasing returns to scale production f (K, L)
(a) more than doubles when you double labor input L;
(b) less than doubles when you triple all inputs;
(c) more than doubles when you double all inputs;
(d) at least triples if you double all inputs. 1Hint: You need to figure out first how much capital is being used when the output is 12 units and labor is 6 or 