The Road Highway Construction Company fixes potholes in interstate highways. The crew fixes potholes using workers and shovels in 1 to 1 correspondence. A worker with 1 shovel can fill 8 potholes in a day. Workers with two - 10 potholes, as can two workers with 1 shovel. Draw the production isoquant corresponding to filling 40 potholes. Draw isocost lines if shovels are $3 and workers are getting paid $30. What is the minimum cost to fill 40 potholes? If shovels become $5, how will the above answers change? What will happen to the composition of inputs?

Now, let's say that the Road Highway Construction Company has the following production function Q = f (K, L) = 15K^0.25L^0.75 where Q is the number of potholes filled, K is the number of shovels, and L is the number of workers. In this case, we do not know anything about shovel-worker ration. The company currently has 15 shovels. What is the Road Highway Construction Company's production function? Graph the production function, with workers on the horizontal axis and output on the vertical axis. (Hint: pick a few random values for L). Determine the average and marginal products of workers at each label of labor you picked to draw the above production function. Show what happens to total, marginal, and average products if 2 shovels break. What do the company's long-run total cost curve and long-run average total cost curve look like? How do the long-run curves change if the production function becomes Q = KL