1-) Assume you have the following production function:
Q = aK + bL
where K is capital, L is labor, ?? is the sum of the digits of the day and b is the sum of last two digits of the year you were born. (If you were born in February 24, 1969, then ?? is 6 and b is15)(You do not have to write your date of birth). Each unit of capital (K) is $1 and each unit of labor(L) is $2. Answer the following based on the production function.
a. What is a and b?
b. What is your total product when K=20 and L is 8?
c. What is the Marginal Product of Capital when K is 20?
d. What is the Marginal Product of Labor when L is 8?
e. If you were to increase your production, will you increase your capital or hire more labor?
f. Draw the isocost for $50 of budget. This means that you need to show all possible combinations of capital (K) and labor(L) that will cost you $50 in total. Show at least two points on the isocost.
g. Draw the isoquant for 50 units of output. This means that you need to show all possible combinations of Capital (K) and Labor (L) that will produce 50 units. Show at least 2 points clearly on the isoquant.
h. If you try to maximize production using $50 only, what combination of labor and capital do you need to employ? Please show it on the isocost and isoquant graph.