An agricultural firm has a production function (products of the whole year) given by q = 500 SQRT(SF). q is output of agricultural products in pounds. S is land area in square feet. F is number of farmers working.
a. Find the best way to produce 5000 pounds of products in a year when farmers’ wage is $10000 per year and land rental rate is $100 per square feet per year. What is the total cost to produce?
b. Find the best way to produce 10000 pounds of products in a year when farmers’ wage is $10000 per year and land rental rate is $100 per square feet per year. What is the total cost to produce?
c. Find the best way to produce 20000 pounds of products in a year when farmers’ wage is $10000 per year and land rental rate is $100 per square feet per year. What is the total cost to produce?
d. Draw the isoquant curves map. Find the best combination of F and S to produce 5000 pounds on the graph. Use horizontal axis for F and vertical axis for S.
e. From parts a, b and c could you find the total cost function? Write down this function.
f. From part e, calculate AC, MC functions. Is the production of these firm constant/increasing/decreasing returns to scale?