Yvetteís Yard Service (YYS) is a company that provideslawn mowing services. Suppose that the only way to mow one lawn is forone worker to use one lawn mower for one day. Two workers with one lawnmower, or one worker with two lawn mowers, can still only mow one lawnper day.(a) (4 marks) Draw the (one-)unit isoquant for YYS and assuming thatYYSíproduction technology exhibits constant returns to scale, drawa couple more isoquants.(b) (6 marks) Assuming that YYS rents lawn mowers for $4 per dayand pays workers $6 per day, draw some of the isocosts for YYS andillustrate the derivation of the output expansion path for YYS at theseprices.(c) (7 marks) Still under the assumption that YYS rents lawn mowersfor $4 per day and pays workers $6 per day, suppose that YYS hasentered into a contract to rent exactly Öve lawn mowers for today, sothe only factor YYS can vary in the short run (that is, today) is thenumber of workers they engage to mow lawns today. Determine thefollowing:total product of labor, marginal product of labor, average productof labor, short-run total cost, short-run variable cost, short-run Öxedcost, short-run average cost, short-run variable cost, short-run averageÖxed cost, short-run marginal cost.(d) (8 marks) For an arbitrary (daily) rental rate for lawn mowers ofr and (daily) wage rate of w per worker derive the long-run totalcost function, the long-run average cost and long-run marginal costfunction.2

This is a complex economics problem that involves understanding of concepts such as isoquants, isocosts, output expansion path, total product of labor, marginal product of labor, average product of labor, short-run total cost, short-run variable cost, short-run fixed cost, short-run average cost, short-run average fixed cost, short-run marginal cost, long-run total cost function, long-run average cost and long-run marginal cost function.

(a) An isoquant is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs. In this case, the isoquant would be a straight line because one worker with one lawn mower can mow one lawn per day. Additional workers or lawn mowers do not increase the output. If YYS's production technology exhibits constant returns to scale, all isoquants would be parallel straight lines.

(b) Isocosts are lines that represent the cost of producing a certain level of output. In this case, the cost of a worker is $6 per day and the cost of a lawn mower is$4 per day. The isocost line would be a straight line with a slope of -6/4 = -1.5. The output expansion path is the line that connects the points of tangency between the isoquants and the isocost lines.

(c) The total product of labor is the total output produced by workers. In this case, it would be the number of lawns mowed. The marginal product of labor is the additional output produced by hiring one more worker. The average product of labor is the total product of labor divided by the number of workers. The short-run total cost is the total cost of production in the short run, which includes both fixed and variable costs. The short-run variable cost is the cost of the variable inputs (workers in this case). The short-run fixed cost is the cost of the fixed inputs (lawn mowers in this case). The short-run average cost is the short-run total cost divided by the quantity of output. The short-run average fixed cost is the short-run fixed cost divided by the quantity of output. The short-run marginal cost is the change in short-run total cost resulting from a one-unit change in output.

(d) The long-run total cost function is the cost of producing a certain level of output in the long run, when all inputs are variable. The long-run average cost is the long-run total cost divided by the quantity of output. The long-run marginal cost is the change in long-run total cost resulting from a one-unit change in output. These would be derived based on the daily rental rate for lawn mowers (r) and the daily wage rate of workers (w).