(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

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

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

Discuss the relationship between short-run average variablecost and short-run marginal cost.(e) (1 mark) Discuss the relationship between short-run total variablecost, short-run total Öxed cost, and short-run total cost.(f ) (4 marks)Discuss the relationship between short-run average variablecost, short-run average Öxed cost, and short-run average total cost

Nimbus Ltd makes brooms and then sells them door-to-door.Here is the relationship between the number of workers and Nimbus's output during a given day. Workers: 0, 1, 2, 3, 4, 5, 6, 7 Output: 0, 20, 50, 90, 120, 140, 150, 155 Marginal product: ? Total cost: Average total cost: Marginal cost: a) Fill in the column of marginal products.What pattern do you see? How might you explain it? b) A worker costs $100 a day and the firm has fixed costs of $200. Use this information to fill in the column for total cost. c) Fill in the column for average total cost.(Recall that ATC=TC/Q.)What pattern do you see? d) Now fill in the column for marginal cost. (Recall that MC=ΔTC/ΔQ.)What pattern do you see? e) Compare the column for marginal product with the column for marginal cost. Explain the relationship. f) Compare the column for average total cost with the column for marginal cost.Explain the relationship.

(b) (If you would like to, you can do part (c) first and use your answer to (c) to answerthis question.) Find the total cost of producing 32 units of output.(c) Find the total cost, average cost and marginal cost of producing y units of output.Is the average cost increasing or decreasing in y? Is the marginal cost higher or lowerthan the average cost?